Quiver Hecke superalgebras

By Seok-Jin Kang, Masaki Kashiwara, Shunsuke Tsuchioka. 2011

74 citations recorded by the source corpus.

We introduce a new family of superalgebras which should be considered as a super version of the Khovanov-Lauda-Rouquier algebras. Let $I$ be the set of vertices of a Dynkin diagram with parity. To this data, we associate a family of graded superalgebras, the quiver Hecke superalgebras. When there are no odd vertices, these algebras are nothing but the usual Khovanov-Lauda-Rouquier algebras. We then define another family of graded superalgebras, the quiver Hecke-Clifford superalgebras, and show that they are weakly Morita superequivalent to the quiver Hecke superalgebras. Moreover, we prove that the affine Hecke-Clifford superalgebras, as well as their degenerate version, the affine Sergeev superalgebras, are isomorphic to the quiver Hecke-Clifford superalgebras after a completion.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ef94f5731fda7386ded77898f7f2397c6c5fd4d5

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In Discrete Mathematics and Combinatorics

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Citations in the corpus

Affine highest weight categories and affine quasihereditary algebras (2014, unknown): “nd Sazdanovich [29] used to category Hermite polynomials seem to be B-highest weight for B the class of nilCoxeter algebras. The odd nilHecke algebras [19] and quiver Hecke(-Cliﬀord) superalgebras of [22] should satisfy the (super analogue of) the axioms of B-quasihereditary for a class B of algebra”
The Odd nilHecke Algebra and its Diagrammatics (2011, result): “cular, we have an isomorphism U+ q (sl2)A →K0(ONH) (6.3) ϑ(a) →E(a) where U + q (sl2)A is the integral version of the algebra Uq (sl2). The same result was announced by Kang, Kashiwara, and Tsuchioka [2]. Denote by ONHN := LN a=0 ONH N a the direct sum of cyclotomic quotients of ONHa. The odd Grassm”