scholarly journals Kirillov’s character formula, the holomorphic Peter–Weyl theorem, and the Blattner–Kostant–Sternberg pairing

2008 ◽  
Vol 58 (7) ◽  
pp. 833-848 ◽  
Author(s):  
Johannes Huebschmann
Keyword(s):  
Character Formula ◽  
Weyl Theorem

scholarly journals Descents of λ-unimodal cycles in a character formula

2016 ◽  
Vol 339 (10) ◽  
pp. 2399-2409
Author(s):  
Kassie Archer
Keyword(s):  
Character Formula

scholarly journals The elliptic Weyl character formula

2014 ◽  
Vol 150 (7) ◽  
pp. 1196-1234 ◽  
Author(s):  
Nora Ganter
Keyword(s):  
Line Bundle ◽  
Lie Groups ◽  
Theoretical Framework ◽  
Flag Variety ◽  
Schubert Calculus ◽  
Character Formula ◽  
Elliptic Cohomology ◽  
Image Position ◽  
Weyl Character Formula

AbstractWe calculate equivariant elliptic cohomology of the partial flag variety$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}G/H$, where$H\subseteq G$are compact connected Lie groups of equal rank. We identify the${\rm RO}(G)$-graded coefficients${\mathcal{E}} ll_G^*$as powers of Looijenga’s line bundle and prove that transfer along the map$$\begin{equation*} \pi \,{:}\,G/H\longrightarrow {\rm pt} \end{equation*}$$is calculated by the Weyl–Kac character formula. Treating ordinary cohomology,$K$-theory and elliptic cohomology in parallel, this paper organizes the theoretical framework for the elliptic Schubert calculus of [N. Ganter and A. Ram,Elliptic Schubert calculus, in preparation].

On the Weyl character formula forSU(n)

1976 ◽  
Vol 15 (3) ◽  
pp. 201-206 ◽  
Author(s):  
R. J. Plymen
Keyword(s):  
Character Formula ◽  
Weyl Character Formula

Derived length when a product of characters has two nonprincipal irreducible constituents

2016 ◽  
Vol 15 (06) ◽  
pp. 1650110
Author(s):  
Lisa Rose Hendrixson ◽  
Mark L. Lewis
Keyword(s):  
Solvable Group ◽  
Irreducible Character ◽  
Character Formula ◽  
Derived Length

We study the situation where a solvable group [Formula: see text] has a faithful irreducible character [Formula: see text] such that [Formula: see text] has exactly two distinct nonprincipal irreducible constituents. We prove that [Formula: see text] has derived length bounded above by 8, and provide an example of such a group having derived length 8. In particular, this improves upon a result of Adan-Bante.

scholarly journals On a character formula involving Borel subgroups

1996 ◽  
Vol 247 ◽  
pp. 273-275
Author(s):  
Mihalis Maliakas
Keyword(s):  
Character Formula

scholarly journals Relative version of Weyl-Kac character formula

1990 ◽  
Vol 130 (1) ◽  
pp. 191-197
Author(s):  
Jong-Min Ku
Keyword(s):  
Character Formula ◽  
Relative Version

A Refinement of the Peter-Weyl Theorem

2010 ◽  
pp. 230-237
Author(s):  
George Lusztig
Keyword(s):  
Weyl Theorem

Tokuyama’s Theorem

2011 ◽  
Author(s):  
Ben Brubaker ◽  
Daniel Bump ◽  
Solomon Friedberg
Keyword(s):  
Eisenstein Series ◽  
Whittaker Function ◽  
Character Formula ◽  
Schur Polynomials ◽  
Normalization Constant ◽  
Small Letter ◽  
Weyl Character Formula

This chapter introduces the Tokuyama's Theorem, first by writing the Weyl character formula and restating Schur polynomials, the values of the Whittaker function multiplied by the normalization constant. The λ‎-parts of Whittaker coefficients of Eisenstein series can be profitably regarded as a deformation of the numerator in the Weyl character formula. This leads to deformations of the Weyl character formula. Tokuyama gave such a deformation. It is an expression of ssubscript Greek small letter lamda(z) as a ratio of a numerator to a denominator. The denominator is a deformation of the Weyl denominator, and the numerator is a sum over Gelfand-Tsetlin patterns with top row λ‎ + ρ‎.

Sign in / Sign up

Export Citation Format

Share Document