W-ALGEBRAS FROM HEISENBERG CATEGORIES

DOI10.1017/S1474748016000189zbMath1405.81045arXiv1501.00589MaRDI QIDQ4691765

Sabin Cautis, Aaron D. Lauda, Joshua Sussan, Anthony M. Licata

Publication date: 24 October 2018

Published in: Journal of the Institute of Mathematics of Jussieu (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.00589

zbMATH Keywords

traceHeisenberg algebraHochschild homologycategorificationW-algebrasHeisenberg category

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Infinite-dimensional Lie (super)algebras (17B65) Bergman spaces and Fock spaces (30H20)

Related Items (13)

The elliptic Hall algebra and the deformed Khovanov Heisenberg category ⋮ An equivalence between truncations of categorified quantum groups and Heisenberg categories ⋮ Frobenius W-algebras and traces of Frobenius Heisenberg categories ⋮ Trace of the twisted Heisenberg category ⋮ Categorification and applications ⋮ Trace decategorification of the Hecke category ⋮ Trace decategorification of tensor product algebras ⋮ Quantum Frobenius Heisenberg categorification ⋮ The center of the twisted Heisenberg category, factorial Schur \(Q\)-functions, and transition functions on the Schur graph ⋮ Khovanov's Heisenberg category, moments in free probability, and shifted symmetric functions ⋮ On the definition of Heisenberg category ⋮ Embedding Deligne's category \(\underline{\mathrm{Re}}\mathrm{p}(S_t)\) in the Heisenberg category (with an appendix written with Christopher Ryba) ⋮ String diagrams and categorification

Cites Work

• Cherednik algebras, \(W\)-algebras and the equivariant cohomology of the moduli space of instantons on \(\mathbb A^2\)
• Trace as an alternative decategorification functor
• Determinant formulae of quasi-finite representation of \(W_{1+\infty}\) algebra at lower levels
• Homology of graded Hecke algebras.
• Quasifinite representations of classical Lie subalgebras of \({\mathcal W}_{1+\infty}\)
• Heisenberg categorification and Hilbert schemes
• \({\mathcal W}_{1+\infty}\) and \({\mathcal W}(gl_ N)\) with central charge \(N\)
• Quantum affine algebras and deformations of the Virasoro and \({\mathcal W}\)-algebras
• Polynomial functors and categorifications of Fock space. II
• On a categorical Boson-Fermion correspondence
• A categorification of quantum \(\text{sl}(n)\)
• A Presentation of the Deformed W 1+∞ Algebra
• Vertex algebras and the class algebras of wreath products
• Heisenberg algebra and a graphical calculus
• Virasoro algebra and wreath product convolution
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