A cohomological interpretation of archimedean zeta integrals for $$\mathrm{GL}_3\times \mathrm{GL}_2$$

2021 ◽  
Vol 7 (4) ◽  
Author(s):  
Takashi Hara ◽  
Kenichi Namikawa
Keyword(s):  
Cohomological Interpretation

scholarly journals The $Z$-Polynomial of a Matroid

10.37236/7105 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Nicholas Proudfoot ◽  
Yuan Xu ◽  
Ben Young
Keyword(s):  
Closed Formula ◽  
Poincaré Duality ◽  
Poincare Duality ◽  
Whitney Numbers ◽  
Alternating Sums ◽  
Cohomological Interpretation

We introduce the $Z$-polynomial of a matroid, which we define in terms of the Kazhdan-Lusztig polynomial. We then exploit a symmetry of the $Z$-polynomial to derive a new recursion for Kazhdan-Lusztig coefficients. We solve this recursion, obtaining a closed formula for Kazhdan-Lusztig coefficients as alternating sums of multi-indexed Whitney numbers. For realizable matroids, we give a cohomological interpretation of the $Z$-polynomial in which the symmetry is a manifestation of Poincaré duality.

scholarly journals A cohomological interpretation of Bogomolov’s instability

2013 ◽  
Vol 141 (9) ◽  
pp. 3049-3053 ◽  
Author(s):  
Gabriele Di Cerbo
Keyword(s):  
Cohomological Interpretation

scholarly journals A COHOMOLOGICAL INTERPRETATION OF THE MIGDAL–MAKEENKO EQUATIONS

2002 ◽  
Vol 17 (08) ◽  
pp. 481-489 ◽  
Author(s):  
A. AGARWAL ◽  
S. G. RAJEEV
Keyword(s):  
Lie Algebra ◽  
Equations Of Motion ◽  
Generating Functional ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Change Of Variables ◽  
Anomalous Term ◽  
Large N ◽  
Infinite Dimensional Lie Algebra ◽  
Cohomological Interpretation

The equations of motion of quantum Yang–Mills theory (in the planar "large-N" limit), when formulated in loop-space are shown to have an anomalous term, which makes them analogous to the equations of motion of WZW models. The anomaly is the Jacobian of the change of variables from the usual ones, i.e. the connection one-form A, to the holonomy U. An infinite-dimensional Lie algebra related to this change of variables (the Lie algebra of loop substitutions) is developed, and the anomaly is interpreted as an element of the first cohomology of this Lie algebra. The Migdal–Makeenko equations are shown to be the condition for the invariance of the Yang–Mills generating functional Z under the action of the generators of this Lie algebra. Connections of this formalism to the collective field approach of Jevicki and Sakita are also discussed.

A cohomological interpretation of the graded brauer group I

1983 ◽  
Vol 11 (19) ◽  
pp. 2129-2149 ◽  
Author(s):  
S. Caenpeel
Keyword(s):  
Brauer Group ◽  
Group I ◽  
Cohomological Interpretation

Linearizing Flows and a Cohomological Interpretation of Lax Equations

1985 ◽  
Vol 107 (6) ◽  
pp. 1445 ◽  
Author(s):  
Phillip A. Griffiths
Keyword(s):  
Lax Equations ◽  
Cohomological Interpretation

scholarly journals Selmer groups and class groups

2014 ◽  
Vol 151 (3) ◽  
pp. 416-434 ◽  
Author(s):  
Kęstutis Česnavičius
Keyword(s):  
Number Fields ◽  
Torsion Subgroup ◽  
Selmer Groups ◽  
Ideal Class Group ◽  
Class Groups ◽  
New Approach ◽  
Quadratic Extensions ◽  
Iwasawa Invariants ◽  
Cohomological Interpretation ◽  
The Ideal

AbstractLet $A$ be an abelian variety over a global field $K$ of characteristic $p\geqslant 0$. If $A$ has nontrivial (respectively full) $K$-rational $l$-torsion for a prime $l\neq p$, we exploit the fppf cohomological interpretation of the $l$-Selmer group $\text{Sel}_{l}\,A$ to bound $\#\text{Sel}_{l}\,A$ from below (respectively above) in terms of the cardinality of the $l$-torsion subgroup of the ideal class group of $K$. Applied over families of finite extensions of $K$, the bounds relate the growth of Selmer groups and class groups. For function fields, this technique proves the unboundedness of $l$-ranks of class groups of quadratic extensions of every $K$ containing a fixed finite field $\mathbb{F}_{p^{n}}$ (depending on $l$). For number fields, it suggests a new approach to the Iwasawa ${\it\mu}=0$ conjecture through inequalities, valid when $A(K)[l]\neq 0$, between Iwasawa invariants governing the growth of Selmer groups and class groups in a $\mathbb{Z}_{l}$-extension.

Cohomological Interpretation of the Motivic Zeta Function

2016 ◽  
pp. 129-140
Author(s):  
Lars Halvard Halle ◽  
Johannes Nicaise
Keyword(s):  
Zeta Function ◽  
Cohomological Interpretation ◽  
Motivic Zeta Function

scholarly journals SIMPLE CURRENT EXTENSIONS AND MAPPING CLASS GROUP REPRESENTATIONS

1998 ◽  
Vol 13 (02) ◽  
pp. 199-207 ◽  
Author(s):  
PETER BANTAY
Keyword(s):  
Fixed Point ◽  
Mapping Class Group ◽  
Class Group ◽  
Mapping Class ◽  
Group Representations ◽  
Cohomological Interpretation

The conjecture of Fuchs, Schellekens and Schweigert on the relation of mapping class group representations and fixed point resolution in simple current extensions is investigated, and a cohomological interpretation of the untwisted stabilizer is given.

THE AMITSUR–LEVITZKI THEOREM FOR THE ORTHOSYMPLECTIC LIE SUPERALGEBRA 𝔬𝔰𝔭(1, 2n)

2006 ◽  
Vol 05 (03) ◽  
pp. 307-332
Author(s):  
PIERRE-ALEXANDRE GIÉ ◽  
GEORGES PINCZON ◽  
ROSANE USHIROBIRA
Keyword(s):  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Orthosymplectic Lie Superalgebra ◽  
Cohomological Interpretation

Based on Kostant's cohomological interpretation of the Amitsur–Levitzki theorem, we prove a super version of this theorem for the Lie superalgebras 𝔬𝔰𝔭(1, 2n). We conjecture that no other classical Lie superalgebra can satisfy an Amitsur–Levitzki type super identity. We show several (super) identities for the standard super polynomials. Finally, a combinatorial conjecture on the standard skew supersymmetric polynomials is stated.

scholarly journals A cohomological interpretation of Brion’s formula

2007 ◽  
Vol 9 (2) ◽  
pp. 321-336
Author(s):  
Thomas Hüttermann
Keyword(s):  
Cohomological Interpretation
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