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Quantum Hamiltonian reduction of W-algebras and category O

Authors :
Morgan, Stephen
Publication Year :
2015

Abstract

We define a quantum version of Hamiltonian reduction by stages, producing a construction in type A for a quantum Hamiltonian reduction from the W-algebra $U(\mathfrak{g},e_1)$ to an algebra conjecturally isomorphic to $U(\mathfrak{g},e_2)$, whenever $e_2 \ge e_1$ in the dominance ordering. This isomorphism is shown to hold whenever $e_1$ is subregular, and in $\mathfrak{sl}_n$ for all $n \le 4$. We next define embeddings of various categories $\mathcal{O}$ for the W-algebras associated to $e_1$ and $e_2$, amongst them the embeddings $\mathcal{O}(e_2,\mathfrak{p}) \hookrightarrow \mathcal{O}(e_1,\mathfrak{p})$, where $\mathfrak{p}$ is a parabolic subalgebra containing both $e_1$ and $e_2$ in its Levi subalgebra.<br />Comment: 22 pages. This is the journal version of my PhD thesis (arXiv:1502.07025 [math.RT]) with extended results

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1510.07352
Document Type :
Working Paper