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December 2019 A Fock space model for decomposition numbers for quantum groups at roots of unity
Martina Lanini, Arun Ram, Paul Sobaje
Kyoto J. Math. 59(4): 955-991 (December 2019). DOI: 10.1215/21562261-2019-0031


In this paper we construct an abstract Fock space for general Lie types that serves as a generalization of the infinite wedge q-Fock space familiar in type A. Specifically, for each positive integer , we define a Z[q,q1]-module F with bar involution by specifying generators and straightening relations adapted from those appearing in the Kashiwara–Miwa–Stern formulation of the q-Fock space. By relating F to the corresponding affine Hecke algebra, we show that the abstract Fock space has standard and canonical bases for which the transition matrix produces parabolic affine Kazhdan–Lusztig polynomials. This property and the convenient combinatorial labeling of bases of F by dominant integral weights makes F a useful combinatorial tool for determining decomposition numbers of Weyl modules for quantum groups at roots of unity.


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Martina Lanini. Arun Ram. Paul Sobaje. "A Fock space model for decomposition numbers for quantum groups at roots of unity." Kyoto J. Math. 59 (4) 955 - 991, December 2019.


Received: 30 December 2016; Revised: 21 February 2017; Accepted: 22 June 2017; Published: December 2019
First available in Project Euclid: 22 October 2019

zbMATH: 07194002
MathSciNet: MR4032204
Digital Object Identifier: 10.1215/21562261-2019-0031

Primary: 17B37
Secondary: 20C20

Keywords: Fock space , Hecke algebra , multiplicity formulas , quantum groups

Rights: Copyright © 2019 Kyoto University


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Vol.59 • No. 4 • December 2019
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