2020
DOI: 10.48550/arxiv.2004.13082
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The modular Weyl-Kac character formula

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Cited by 3 publications
(6 citation statements)
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“…Proof. The statements (1) through (6) and examples of existence of all cases follow from the case-by-case examinations in the proof of Proposition 4.1 together with Theorem 1.1. Theorem 1.4 is the same statement in the language of supports by [25].…”
Section: 2mentioning
confidence: 78%
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“…Proof. The statements (1) through (6) and examples of existence of all cases follow from the case-by-case examinations in the proof of Proposition 4.1 together with Theorem 1.1. Theorem 1.4 is the same statement in the language of supports by [25].…”
Section: 2mentioning
confidence: 78%
“…It is often possible to write explicit bases for the unitary representations or for the corresponding representations of closely related algebras such as the Morita equivalent diagrammatic Cherednik algebra or the Hecke algebra. 1 At the categorical level, the unitary irreducible representations in type A, and for certain parameters, type G(ℓ, 1, n), have been proven to possess resolutions by complexes of direct sums of standard modules [4], [7], [6]. Such resolutions, known in the literature as BGG resolutions, categorify character formulas via the Euler characteristic of the complex.…”
Section: Motivation and Summary Of Resultsmentioning
confidence: 99%
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“…At the categorical level, the unitary irreducible representations in type A, and for certain parameters, type G( , 1, n), have been proved to possess resolutions by complexes of direct sums of standard modules [1,6,7]. Such resolutions, known in the literature as Bernstein-Gelfand-Gelfand (BGG) resolutions, categorify character formulas via the Euler characteristic of the complex.…”
Section: Motivationmentioning
confidence: 99%
“…Aspects of this story should be very familiar to the experts: we have an algebraic object (in this case a cyclotomic or affine Hecke algebra) for which there exists a "nice family" of irreducible representations (in this case, the unitary representations) which can be combinatorially classified and constructed via explicit bases and BGG resolutions. Analogous stories exist for ladder representations of p-adic groups [BC15], finite dimensional representations of (Kac-Moody) Lie algebras [BGG75,KK79], and homogeneous representations of antispherical Hecke categories [BHN20].…”
Section: Introductionmentioning
confidence: 99%