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Quantum affine
algebras, canonical bases, and q-deformation of arithmetical functions
Henry H. Kim and Kyu-Hwan Lee |
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Vol. 255 (2012), No. 2, 393–415
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Abstract |
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We obtain affine analogs of the Gindikin–Karpelevich and Casselman–Shalika formulas as sums over Kashiwara and Lusztig’s canonical bases. As suggested by these formulas, we define natural q-deformation of arithmetical functions such as (multi)partition functions and Ramanujan τ-functions, and prove various identities among them. In some examples we recover classical identities by taking limits. Additionally, we consider q-deformation of the Kostant function and study certain q-polynomials whose special values are weight multiplicities. |
Keywords
quantum affine algebras, canonical bases, q-deformation of
arithmetic functions
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Mathematical Subject Classification 2010
Primary: 17B37
Secondary: 05E10
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Milestones
Received: 24 January 2011
Accepted: 7 June 2011
Published: 10 April 2012
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Authors |
| Henry H. Kim | |
| Department of Mathematics University of Toronto Toronto, Ontario M5S2E4 Canada |
Korea Institute for Advanced
Study Seoul Korea |
| Kyu-Hwan Lee | |
| Department of Mathematics University of Connecticut Storrs, CT 06269-3009 United States |
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