Generalized exponents of small representations. II
Author:
Bogdan Ion
Journal:
Represent. Theory 15 (2011), 433493
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 nonnegative formulas for generalized exponents of small representations in all types. It contains a first formula for generalized exponents of small weights which extends the ShapiroSteinberg 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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Bogdan
Ion, The Cherednik kernel and generalized exponents, Int.
Math. Res. Not. 36 (2004), 1869–1895. MR 2058356
(2005a:17004), http://dx.doi.org/10.1155/S1073792804133485
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Ion, Generalized exponents of small representations. I,
Represent. Theory 13 (2009), 401–426. MR 2540703
(2010i:17013), http://dx.doi.org/10.1090/S1088416509003598
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B. Ion, Generalized exponents of small representations. III. In preparation.
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G. Kac, Infinite root systems, representations of graphs and
invariant theory, Invent. Math. 56 (1980),
no. 1, 57–92. MR 557581
(82j:16050), http://dx.doi.org/10.1007/BF01403155
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 N. Bourbaki, Lie groups and Lie algebras. Chapters 46. Elements of Mathematics. SpringerVerlag, Berlin, 2002. MR 1890629 (2003a:17001)
 2.
 B. Ion, The Cherednik kernel and generalized exponents. Int. Math. Res. Not. 2004, no. 36, 18691895. MR 2058356 (2005a:17004)
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 B. Ion, Generalized exponents of small representations. I. Represent. Theory 13 (2009), 401426. MR 2540703
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 B. Ion, Generalized exponents of small representations. III. In preparation.
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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/S108841652011003721
PII:
S 10884165(2011)003721
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.
