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Hecke-Clifford superalgebras, crystals of type \(A_{2\ell}^{(2)}\) and modular branching rules for \(\widehat{S}_n\). (English) Zbl 1005.17010
Summary: This paper is concerned with the modular representation theory of the affine Hecke-Clifford superalgebra, the cyclotomic Hecke-Clifford superalgebras, and projective representations of the symmetric group. Our approach exploits crystal graphs of affine Kac-Moody algebras.

MSC:
17B37 Quantum groups (quantized enveloping algebras) and related deformations
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
20C20 Modular representations and characters
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
20C08 Hecke algebras and their representations
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