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Character expansion
of Kac–Moody correction factors
Kyu-Hwan Lee, Dongwen Liu and Thomas Oliver |
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Vol. 313 (2021), No. 1, 159–183
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DOI: 10.2140/pjm.2021.313.159
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Abstract |
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A correction factor naturally arises in the theory of -adic Kac–Moody groups. We expand the correction factor into a sum of irreducible characters of the underlying Kac–Moody algebra. We derive a formula for the coefficients which lie in the ring of power series with integral coefficients. In the case that the Weyl group is a universal Coxeter group, we show that the coefficients are actually polynomials. |
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Keywords
Kac–Moody algebras, Weyl groups, Poincare series, Macdonald
identity, correction factor, character expansions, Coxeter
groups
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Mathematical Subject Classification 2010
Primary: 17B22, 17B67
Secondary: 05E10
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Milestones
Received: 22 February 2020
Revised: 30 April 2021
Accepted: 12 June 2021
Published: 17 September 2021
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Authors |
| Kyu-Hwan Lee | |
| Department of Mathematics University of Connecticut Storrs, CT United States |
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| Dongwen Liu | |
| School of Mathematical
Sciences Zhejiang University Hangzhou China |
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| Thomas Oliver | |
| School of Mathematical
Sciences University of Nottingham Nottingham United Kingdom |
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