A general approach to Heisenberg categorification via wreath product algebras

作者：Rosso Daniele; Savage Alistair^*

来源：Mathematische Zeitschrift, 2017, 286(1-2): 603-655.

DOI：10.1007/s00209-016-1776-9

• Categorification
• Lattice Heisenberg algebra
• Tower of algebras
• Graded Frobenius superalgebra
• Fock space

We associate a monoidal category H-B , defined in terms of planar diagrams, to any graded Frobenius superalgebra B. This category acts naturally on modules over the wreath product algebras associated to B. To B we also associate a (quantum) lattice Heisenberg algebra h(B). We show that, provided B is not concentrated in degree zero, the Grothendieck group of H-B is isomorphic, as an algebra, to h(B). For specific choices of Frobenius algebra B, we recover existing results, including those of Khovanov and Cautis-Licata. We also prove that certain morphism spaces in the category H-B contain generalizations of the degenerate affine Hecke algebra. Specializing B, this proves an open conjecture of Cautis-Licata.

• 出版日期2017-6