scholarly journals Residues of intertwining operators for SO*6 as character identities

2010 ◽  
Vol 146 (3) ◽  
pp. 772-794 ◽  
Author(s):  
Freydoon Shahidi ◽  
Steven Spallone
Keyword(s):  
Quadratic Extension ◽  
The Other ◽  
Levi Subgroup ◽  
Intertwining Operators ◽  
Central Character ◽  
Supercuspidal Representation ◽  
Induced Representations ◽  
Intertwining Operator ◽  
Other Hand ◽  
Hilbert’S Theorem 90

AbstractWe show that the residue at s=0 of the standard intertwining operator attached to a supercuspidal representation π⊗χ of the Levi subgroup GL2(F)×E1 of the quasisplit group SO*6(F) defined by a quadratic extension E/F of p-adic fields is proportional to the pairing of the characters of these representations considered on the graph of the norm map of Kottwitz–Shelstad. Here π is self-dual, and the norm is simply that of Hilbert’s theorem 90. The pairing can be carried over to a pairing between the character on E1 and the character on E× defining the representation of GL2(F) when the central character of the representation is quadratic, but non-trivial, through the character identities of Labesse–Langlands. If the quadratic extension defining the representation on GL2(F) is different from E the residue is then zero. On the other hand when the central character is trivial the residue is never zero. The results agree completely with the theory of twisted endoscopy and L-functions and determines fully the reducibility of corresponding induced representations for all s.

scholarly journals On axiomatic approaches to intertwining operator algebras

2016 ◽  
Vol 18 (04) ◽  
pp. 1550051 ◽  
Author(s):  
Ling Chen
Keyword(s):  
Vertex Operator ◽  
Jacobi Identity ◽  
Operator Algebras ◽  
The Other ◽  
Intertwining Operators ◽  
Genus Zero ◽  
Intertwining Operator ◽  
Irreducible Modules ◽  
Axiomatic Approaches

We study intertwining operator algebras introduced and constructed by Huang. In the case that the intertwining operator algebras involve intertwining operators among irreducible modules for their vertex operator subalgebras, a number of results on intertwining operator algebras were given in [Y.-Z. Huang, Generalized rationality and a “Jacobi identity” for intertwining operator algebras, Selecta Math. (N.S.) 6 (2000) 225–267] but some of the proofs were postponed to an unpublished monograph. In this paper, we give the proofs of these results in [Y.-Z. Huang, Generalized rationality and a “Jacobi identity” for intertwining operator algebras, Selecta Math. (N.S.) 6 (2000) 225–267] and we formulate and prove results for general intertwining operator algebras without assuming that the modules involved are irreducible. In particular, we construct fusing and braiding isomorphisms for general intertwining operator algebras and prove that they satisfy the genus-zero Moore–Seiberg equations. We show that the Jacobi identity for intertwining operator algebras is equivalent to generalized rationality, commutativity and associativity properties of intertwining operator algebras. We introduce the locality for intertwining operator algebras and show that the Jacobi identity is equivalent to the locality, assuming that other axioms hold. Moreover, we establish that any two of the three properties, associativity, commutativity and skew-symmetry, imply the other (except that when deriving skew-symmetry from associativity and commutativity, more conditions are needed). Finally, we show that three definitions of intertwining operator algebras are equivalent.

Cyborg Affect and the Power of the Posthuman in the Ghost in the Shell Franchise

Noir Affect ◽  
2020 ◽  
pp. 156-177
Author(s):  
Peter Hitchcock
Keyword(s):  
Free Association ◽  
The Other ◽  
Central Character ◽  
Quarter Century ◽  
Feature Films ◽  
Other Hand ◽  
Old Japanese ◽  
The Media ◽  
Police Procedural ◽  
The One

This chapter explores noir affect in Ghost in a Shell, a quarter-century-old, Japanese manga/anime franchise that spans several series in print, feature films, and television. Whatever the media, the different versions of the narrative conform to standard expectations of adolescent heterosexual masculinism. Yet such elements seem to form the series’ mystical shell rather than the conflicted and contradictory rationality of their central kernel (which itself springs from the serial logic of the noir police procedural). On the one hand, the chapter argues that representational aesthetics necessarily constrain even the radical and free association of an anime subculture; on the other hand, the series critically engages the forms of time articulated in the intersection of cyborg signification and seriality. Cyborg affect does not just ask the familiar question, where does a body end? It also interrogates the terms of technological reproducibility in relationship to political possibility. The synchrony of Major Motoko Kusanagi (the central character/cyborg) holds important lessons for how we read/see affect in relationship to the series, a formation haunted by the ghost of socialization itself.

On the Tempered Spectrum of Quasi-Split Classical Groups II

2001 ◽  
Vol 53 (2) ◽  
pp. 244-277 ◽  
Author(s):  
David Goldberg ◽  
Freydoon Shahidi
Keyword(s):  
Parabolic Subgroup ◽  
Characteristic Zero ◽  
Unitary Group ◽  
Quadratic Extension ◽  
Intertwining Operators ◽  
Classical Groups ◽  
Maximal Parabolic Subgroup ◽  
Supercuspidal Representation

AbstractWe determine the poles of the standard intertwining operators for a maximal parabolic subgroup of the quasi-split unitary group defined by a quadratic extension E/F of p-adic fields of characteristic zero. We study the case where the Levi component M ≃ GLn(E) × Um(F), with n ≡ m (mod 2). This, along with earlier work, determines the poles of the local Rankin-Selberg product L-function L(s, t′ × τ), with t′ an irreducible unitary supercuspidal representation of GLn(E) and τ a generic irreducible unitary supercuspidal representation of Um(F). The results are interpreted using the theory of twisted endoscopy.

scholarly journals Towards a Goldberg–Shahidi pairing for classical groups

2018 ◽  
Vol 30 (2) ◽  
pp. 347-384
Author(s):  
Arnab Mitra ◽  
Steven Spallone
Keyword(s):  
Adjoint Action ◽  
Bilinear Pairing ◽  
Vector Spaces ◽  
Unipotent Radical ◽  
Levi Subgroup ◽  
Intertwining Operators ◽  
Maximal Parabolic Subgroup ◽  
Induced Representations ◽  
Matrix Coefficients ◽  
Symplectic Case

AbstractLet{G^{1}}be an orthogonal, symplectic or unitary group over a local field and let{P=MN}be a maximal parabolic subgroup. Then the Levi subgroupMis the product of a group of the same type as{G^{1}}and a general linear group, acting on vector spacesXandW, respectively. In this paper we decompose the unipotent radicalNofPunder the adjoint action ofM, assuming{\dim W\leq\dim X}, excluding only the symplectic case with{\dim W}odd. The result is a Weyl-type integration formula forNwith applications to the theory of intertwining operators for parabolically induced representations of{G^{1}}. Namely, one obtains a bilinear pairing on matrix coefficients, in the spirit of Goldberg–Shahidi, which detects the presence of poles of these operators at 0.

scholarly journals Analytic vectors in continuousp-adic representations

2009 ◽  
Vol 145 (1) ◽  
pp. 247-270 ◽  
Author(s):  
Tobias Schmidt
Keyword(s):  
Banach Space ◽  
Lie Group ◽  
The Other ◽  
Induced Representations ◽  
Faithful Functor ◽  
Other Hand ◽  
Derived Functors

AbstractGiven a compactp-adic Lie groupGover a finite unramified extensionL/ℚplet GL/ℚpbe the product over all Galois conjugates ofG. We construct an exact and faithful functor from admissibleG-Banach space representations to admissible locallyL-analyticGL/ℚp-representations that coincides with passage to analytic vectors in the caseL=ℚp. On the other hand, we study the functor ‘passage to analytic vectors’ and its derived functors over general basefields. As an application we compute the higher analytic vectors in certain locally analytic induced representations.

The Archimedean Intertwining Operator for GLN

2019 ◽  
pp. 168-210
Author(s):  
Uwe Weselmann
Keyword(s):  
General Setting ◽  
Intertwining Operators ◽  
Induced Representations ◽  
Special Values ◽  
Intertwining Operator

This chapter generalizes an identity conjectured by G. Harder and proved by D. Zagier from the case of GL3(ℝ)-representations to the case of general GLN(ℝ)-representations. These are useful in applying the results of Harder and Anantharam Raghuram on quotients of special values of L-functions. To begin, the chapter provides the general setting for this analysis—the group theoretic data and the induced representations. It then discusses the intertwining operators as well as the J-admissible permutations. The chapter goes on to discuss representations and L-functions before turning to the main theorem on Archimedean intertwining operator. Finally, the chapter discusses some applications to cohomology.

scholarly journals Rajab’s Atlantic Street and Identity Crisis in a Globalized World of Disorientation

2018 ◽  
Vol 1 (1) ◽  
pp. 68-78
Author(s):  
Bhawana Regmi
Keyword(s):  
Cultural Identity ◽  
Identity Crisis ◽  
The Other ◽  
Central Character ◽  
The Novel ◽  
Human Beings ◽  
Cultural Products ◽  
Other Hand ◽  
Globalized World

Human beings have been very protective about their identities. Cultural identity is one of the mechanisms that keep them connected to each other and their roots in the globalized world. This becomes more evident in times of threat and uncertainty about their belonging. Therefore, the issues of identity come to the fore in migration and diaspora discourses. In this article, I draw from Stuart Hall’s idea of identity and argue that irrespective of the socio-cultural disorientation and ethnic prejudices, in which the central character undergoes in the novel and craves for and succeeds in creating an identity. Not only the protagonist but also other characters come together to proclaim their identity which on the other hand establishes Atlantic Street as a novel by Rajab1 that represents ethnic prejudices. However, the prejudices the characters suffer, in turn, help to bring together the characters who suffer and constitute an ethnic bond between them. The inscription of the lack of recognition as human beings, and the pursuit of identity in and through literature respectively, reiterate the fact that both literature and identity are cultural products that are entwined.

A study of cometary eruptions through OH radio-lines

1999 ◽  
Vol 173 ◽  
pp. 249-254
Author(s):  
A.M. Silva ◽  
R.D. Miró
Keyword(s):  
Short Duration ◽  
Growth Curves ◽  
The Other ◽  
Initial Mass ◽  
Radio Lines ◽  
Other Hand ◽  
Sudden Rise

AbstractWe have developed a model for theH2OandOHevolution in a comet outburst, assuming that together with the gas, a distribution of icy grains is ejected. With an initial mass of icy grains of 108kg released, theH2OandOHproductions are increased up to a factor two, and the growth curves change drastically in the first two days. The model is applied to eruptions detected in theOHradio monitorings and fits well with the slow variations in the flux. On the other hand, several events of short duration appear, consisting of a sudden rise ofOHflux, followed by a sudden decay on the second day. These apparent short bursts are frequently found as precursors of a more durable eruption. We suggest that both of them are part of a unique eruption, and that the sudden decay is due to collisions that de-excite theOHmaser, when it reaches the Cometopause region located at 1.35 × 105kmfrom the nucleus.

Closing the GAP—A 5Å Scanning Microscope

1969 ◽  
Vol 27 ◽  
pp. 6-7
Author(s):  
A. V. Crewe
Keyword(s):  
Normal Form ◽  
The Other ◽  
Resolving Power ◽  
Scanning Microscope ◽  
Conventional Microscope ◽  
Other Hand ◽  
Closing The Gap ◽  
Thermal Sources ◽  
Better Than ◽  
Transmission Microscope

We have become accustomed to differentiating between the scanning microscope and the conventional transmission microscope according to the resolving power which the two instruments offer. The conventional microscope is capable of a point resolution of a few angstroms and line resolutions of periodic objects of about 1Å. On the other hand, the scanning microscope, in its normal form, is not ordinarily capable of a point resolution better than 100Å. Upon examining reasons for the 100Å limitation, it becomes clear that this is based more on tradition than reason, and in particular, it is a condition imposed upon the microscope by adherence to thermal sources of electrons.

Life Beyond 1MeV

1980 ◽  
Vol 38 ◽  
pp. 30-33
Author(s):  
K.H. Westmacott
Keyword(s):  
Electron Microscopy ◽  
Past Experience ◽  
The Other ◽  
Good Case ◽  
Other Hand ◽  
The U.S

Life beyond 1MeV – like life after 40 – is not too different unless one takes advantage of past experience and is receptive to new opportunities. At first glance, the returns on performing electron microscopy at voltages greater than 1MeV diminish rather rapidly as the curves which describe the well-known advantages of HVEM often tend towards saturation. However, in a country with a significant HVEM capability, a good case can be made for investing in instruments with a range of maximum accelerating voltages. In this regard, the 1.5MeV KRATOS HVEM being installed in Berkeley will complement the other 650KeV, 1MeV, and 1.2MeV instruments currently operating in the U.S. One other consideration suggests that 1.5MeV is an optimum voltage machine – Its additional advantages may be purchased for not much more than a 1MeV instrument. On the other hand, the 3MeV HVEM's which seem to be operated at 2MeV maximum, are much more expensive.

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