Generalized exponents of small representations. II

2009/04/16 by Bogdan Ion, Ion, Bogdan
Mathematics · #17B10 #Advanced Algebra and Geometry #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.0904.2487

openalex publication_date 2009/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is the second paper in a sequence devoted to giving manifestly non-negative formulas for generalized exponents of small representations in all types. It contains a first formula for generalized exponents of small weights which extends the Shapiro-Steinberg formula for classical exponents. The formula is made possible by a computation of Fourier coefficients of the degenerate Cherednik kernel. Unlike the usual partition function coefficients, the answer reflects only the combinatorics of minimal expressions as a sum of roots.

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