Hecke-Clifford superalgebras, crystals of type A_{2l}^{(2)} and modular branching rules for \hat S_n

By Jonathan Brundan, Alexander S. Kleshchev. 2001

53 citations recorded by the source corpus.

Ian Grojnowski has developed a purely algebraic way to connect the representation theory of affine Hecke algebras at an (l+1)-th root of unity to the highest weight theory of the affine Kac-Moody algebra of type A_l^(1). The present article is devoted to extending Grojnowski's machinery to the twisted case: we replace the affine Hecke algebras with the affine Hecke-Clifford superalgebras of Jones and Nazarov, and the Kac-Moody algebra A_l^(1) with the twisted algebra A_2l^(2). In particular, we obtain an algebraic construction purely in terms of the representation theory of Hecke-Clifford superalgebras of the plus part U_\Z^+ of the enveloping algebra, as well as of Kashiwara's highest weight crystals B(\infty) and B(\la) for each dominant weight \la. The results of the article have applications to the modular representation theory of the double covers of the symmeric groups, as was predicted originally by Leclerc and Thibon. In particular, the parametrization of irreducibles, classification of blocks and analogues of the modular branching rules of the symmetric group for the double covers over fields of odd characteristic follow from the special case \lambda = \Lambda_0 of our main results. These matters are discussed in the final section of the paper.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fee8791a0b0d5a4deb61f6cf039d0c75b58bf6d1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

A diagrammatic approach to categorification of quantum groups II (2008, unknown): “This approach was further developed by Grojnowski and Vazirani [17], Vazirani [45], [46], Brundan and Kleshchev [8] 310 MIKHAIL KHOVANOV AND AARON D. LAUDA and others.”
On restrictions of modular spin representations of symmetric and alternating groups (2003, background): “If g ∈ Sn is any element, we denote by ĝ any element in π−1(g).”
A diagrammatic approach to categorification of quantum groups II (2008, unknown): “Similar diagrams are used in the graphical calculus of Jones-Wenzl projectors (see [3]), but the latter has no direct relation to the graphical calculus in our paper.”