Knapp–Stein dimension theorem for finite central covering groups

2020 ◽  
Vol 306 (1) ◽  
pp. 265-280
Author(s):  
Caihua Luo
Keyword(s):  
Covering Groups

scholarly journals Kirillov models for distinguished representations

1989 ◽  
Vol 116 ◽  
pp. 89-110 ◽  
Author(s):  
Courtney Moen
Keyword(s):  
Linear Group ◽  
General Linear Group ◽  
Automorphic Forms ◽  
Principal Series ◽  
Weil Representation ◽  
Local Factors ◽  
Distinguished Representations ◽  
Group A ◽  
Local Representations ◽  
Covering Groups

In the theory of automorphic forms on covering groups of the general linear group, a central role is played by certain local representations which have unique Whittaker models. A representation with this property is called distinguished. In the case of the 2-sheeted cover of GL2, these representations arise as the the local components of generalizations of the classical θ-function. They have been studied thoroughly in [GPS]. The Weil representation provides these representations with a very nice realization, and the local factors attached to these representations can be computed using this realization. It has been shown [KP] that only in the case of a certain 3-sheeted cover do we find other principal series of covering groups of GL2 which have a unique Whittaker model. It is natural to ask if these distinguished representations also have a realization analgous to the Weil representation.

Weights for Covering Groups of Symmetric and Alternating Groups, р ≠ 2

1991 ◽  
Vol 43 (4) ◽  
pp. 792-813 ◽  
Author(s):  
G. O. Michler ◽  
J. B. Olsson
Keyword(s):  
Finite Group ◽  
Representation Theory ◽  
Conjugacy Class ◽  
Finite Groups ◽  
Irreducible Character ◽  
Modular Representation ◽  
Modular Representation Theory ◽  
A Finite Group ◽  
Covering Groups ◽  
Fundamental Paper

In his fundamental paper [1] J. L. Alperin introduced the idea of a weight in modular representation theory of finite groups G. Let p be a prime. A p-subgroup R is called a radical subgroup of G if R = Op(NG(R)). An irreducible character φ of NG(R) is called a weight character if φ is trivial on R and belongs to a p-block of defect zero of NG(R)/R. The G-conjugacy class of the pair (R, φ) is a weight of G. Let b be the p-block of NG(R) containing φ, and let B be p-block of G. A weight (R, φ) is a B-weight for the block B of G if B = bG, which means that B and b correspond under the Brauer homomorphism. Alperin's conjecture on weights asserts that the number l*(B) of B-weights of a p-block B of a finite group G equals the number l(B) of modular characters of B.

scholarly journals Positive energy representations of Sobolev diffeomorphism groups of the circle

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Sebastiano Carpi ◽  
Simone Del Vecchio ◽  
Stefano Iovieno ◽  
Yoh Tanimoto
Keyword(s):  
Unitary Representation ◽  
Von Neumann Algebras ◽  
Universal Covering ◽  
Irreducible Representations ◽  
Positive Energy ◽  
Diffeomorphism Groups ◽  
Von Neumann ◽  
Direct Sum ◽  
Covering Groups

AbstractWe show that any positive energy projective unitary representation of $$\mathrm{Diff}_+(S^1)$$ Diff + ( S 1 ) extends to a strongly continuous projective unitary representation of the fractional Sobolev diffeomorphisms $$\mathcal {D}^s(S^1)$$ D s ( S 1 ) for any real $$s>3$$ s > 3 , and in particular to $$C^k$$ C k -diffeomorphisms $$\mathrm{Diff}_+^k(S^1)$$ Diff + k ( S 1 ) with $$k\ge 4$$ k ≥ 4 . A similar result holds for the universal covering groups provided that the representation is assumed to be a direct sum of irreducibles. As an application we show that a conformal net of von Neumann algebras on $$S^1$$ S 1 is covariant with respect to $$\mathcal {D}^s(S^1)$$ D s ( S 1 ) , $$s > 3$$ s > 3 . Moreover every direct sum of irreducible representations of a conformal net is also $$\mathcal {D}^s(S^1)$$ D s ( S 1 ) -covariant.

scholarly journals Classical Theta Lifts for Higher Metaplectic Covering Groups

2020 ◽  
Vol 30 (6) ◽  
pp. 1531-1582
Author(s):  
Solomon Friedberg ◽  
David Ginzburg
Keyword(s):  
Covering Groups

scholarly journals SPIKES IN COSMIC CRYSTALLOGRAPHY

2002 ◽  
Vol 11 (06) ◽  
pp. 869-891 ◽  
Author(s):  
G. I. GOMERO ◽  
A. F. F. TEIXEIRA ◽  
M. J. REBOUÇCAS ◽  
A. BERNUI
Keyword(s):  
Multiple Images ◽  
Multiply Connected ◽  
Major Consequence ◽  
Statistical Fluctuations ◽  
Covering Group ◽  
Connected Case ◽  
Pair Separation ◽  
Simply Connected ◽  
The Universe ◽  
Covering Groups

If the universe is multiply connected and small the sky shows multiple images of cosmic objects, correlated by the covering group of the 3-manifold used to model it. These correlations were originally thought to manifest as spikes in pair separation histograms (PSH) built from suitable catalogues. Using probability theory we derive an expression for the expected pair separation histogram (EPSH) in a rather general topological-geometrical-observational setting. As a major consequence we show that the spikes of topological origin in PSH's are due to translations, whereas other isometries manifest as tiny deformations of the PSH corresponding to the simply connected case. This result holds for all Robertson–Walker spacetimes and gives rise to two basic corollaries: (i) that PSH's of Euclidean manifolds that have the same translations in their covering groups exhibit identical spike spectra of topological origin, making clear that even if the universe is flat the topological spikes alone are not sufficient for determining its topology; and (ii) that PSH's of hyperbolic 3-manifolds exhibit no spikes of topological origin. These corollaries ensure that cosmic crystallography, as originally formulated, is not a conclusive method for unveiling the shape of the universe. We also present a method that reduces the statistical fluctuations in PSH's built from simulated catalogues.

Automorphic forms on covering groups ofGL(2)

1980 ◽  
Vol 57 (2) ◽  
pp. 119-182 ◽  
Author(s):  
Yuval Z. Flicker
Keyword(s):  
Automorphic Forms ◽  
Covering Groups
Sign in / Sign up

Export Citation Format

Share Document