Generalized exponents of small representations. II

Author:
Bogdan Ion

Journal:
Represent. Theory **15** (2011), 433-493

MSC (2010):
Primary 17B10

DOI:
https://doi.org/10.1090/S1088-4165-2011-00372-1

Published electronically:
May 24, 2011

MathSciNet review:
2540703

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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.

**1.**Nicolas Bourbaki,*Lie groups and Lie algebras. Chapters 4–6*, Elements of Mathematics (Berlin), Springer-Verlag, Berlin, 2002. Translated from the 1968 French original by Andrew Pressley. MR**1890629****2.**Bogdan Ion,*The Cherednik kernel and generalized exponents*, Int. Math. Res. Not.**36**(2004), 1869–1895. MR**2058356**, https://doi.org/10.1155/S1073792804133485**3.**Bogdan Ion,*Generalized exponents of small representations. I*, Represent. Theory**13**(2009), 401–426. MR**2540703**, https://doi.org/10.1090/S1088-4165-09-00359-8**4.**B. Ion, Generalized exponents of small representations. III. In preparation.**5.**V. G. Kac,*Infinite root systems, representations of graphs and invariant theory*, Invent. Math.**56**(1980), no. 1, 57–92. MR**557581**, https://doi.org/10.1007/BF01403155

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Additional Information

**Bogdan Ion**

Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 –and– University of Bucharest, Faculty of Mathematics and Computer Science, Algebra and Number Theory research center, 14 Academiei St., Bucharest, Romania

Email:
bion@pitt.edu

DOI:
https://doi.org/10.1090/S1088-4165-2011-00372-1

Received by editor(s):
October 20, 2009

Received by editor(s) in revised form:
December 10, 2009

Published electronically:
May 24, 2011

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.