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Representation Theory
Representation Theory
ISSN 1088-4165

 

Generalized exponents of small representations. II


Author: Bogdan Ion
Journal: Represent. Theory 15 (2011), 433-493
MSC (2010): Primary 17B10
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.


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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: http://dx.doi.org/10.1090/S1088-4165-2011-00372-1
PII: S 1088-4165(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.