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].

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 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

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.

scholarly journals A geometric q‐character formula for snake modules

2020 ◽  
Vol 102 (2) ◽  
pp. 846-878 ◽  
Author(s):  
Bing Duan ◽  
Ralf Schiffler
Keyword(s):  
Character Formula

scholarly journals On Petersson’s partition limit formula

2020 ◽  
pp. 1-14
Author(s):  
Carlos Castaño-Bernard ◽  
Florian Luca
Keyword(s):  
Quadratic Field ◽  
Character Formula ◽  
Real Quadratic Field ◽  
The Real ◽  
Limit Formula ◽  
Real Quadratic

For each prime [Formula: see text] consider the Legendre character [Formula: see text]. Let [Formula: see text] be the number of partitions of [Formula: see text] into parts [Formula: see text] such that [Formula: see text]. Petersson proved a beautiful limit formula for the ratio of [Formula: see text] to [Formula: see text] as [Formula: see text] expressed in terms of important invariants of the real quadratic field [Formula: see text]. But his proof is not illuminating and Grosswald conjectured a more natural proof using a Tauberian converse of the Stolz–Cesàro theorem. In this paper, we suggest an approach to address Grosswald’s conjecture. We discuss a monotonicity conjecture which looks quite natural in the context of the monotonicity theorems of Bateman–Erdős.

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