Trace of the twisted Heisenberg Category

Abstract

We show that the trace decategorification, or zeroth Hochschild homology, of the twisted Heisenberg category defined by Cautis and Sussan is isomorphic to a quotient of $W^{-}$, a subalgebra of $W_{1+\infty }$ defined by Kac, Wang, and Yan. Our result is a twisted analogue of that by Cautis, Lauda, Licata, and Sussan relating $W_{1+\infty }$ and the trace decategorification of the Heisenberg category.

arXiv commentTo appear in Communications in Math. Physics, 36 pages, tikz diagrams

References in corpus (13)

• W_{1+\infty} and W(gl_N) with central charge N
• On the center of quiver-Hecke algebras
• A general approach to Heisenberg categorification via wreath product algebras
• Trace decategorification of categorified quantum sl(2)
• Trace decategorification of the Hecke category
• Current algebras and categorified quantum groups
• Trace as an alternative decategorification functor
• Determinant Formulae of Quasi-Finite Representation of W_{1+\infty} Algebra at Lower Levels
• On a categorical Boson-Fermion correspondence
• The Elliptic Hall algebra and the deformed Khovanov Heisenberg category
• A graphical calculus for the Jack inner product on symmetric functions
• W-algebras from Heisenberg categories
• Cocenters of Hecke-Clifford and spin Hecke algebras

Cited by in corpus (2)

• Normalized characters of symmetric groups and Boolean cumulants via Khovanov's Heisenberg category
• Frobenius W-algebras and traces of Frobenius Heisenberg categories