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Generalized exponents of small representations. II
Author(s):
Bogdan
Ion
Journal:
Represent. Theory
15
(2011),
433-493.
MSC (2010):
Primary 17B10
Posted:
May 24, 2011
MathSciNet review:
2540703
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References |
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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.
References:
-
- 1.
- N. Bourbaki, Lie groups and Lie algebras. Chapters 4-6. Elements of Mathematics. Springer-Verlag, Berlin, 2002. MR 1890629 (2003a:17001)
- 2.
- B. Ion, The Cherednik kernel and generalized exponents. Int. Math. Res. Not. 2004, no. 36, 1869-1895. MR 2058356 (2005a:17004)
- 3.
- B. Ion, Generalized exponents of small representations. I. Represent. Theory 13 (2009), 401-426. MR 2540703
- 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 (82j:16050)
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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:
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
Posted:
May 24, 2011
Copyright of article:
Copyright
2011,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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