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Mathematics > Quantum Algebra
Title: Affine Yangians and some cosets of non-rectangular $W$-algebras
(Submitted on 28 Apr 2024 (v1), last revised 4 May 2024 (this version, v2))
Abstract: We construct a homomorphism from the affine Yangian associated with $\widehat{\mathfrak{sl}}(q_u-q_{u+1})$ to the universal enveloping algebra of a $W$-algebra associated with $\mathfrak{gl}(\sum_{s=1}^lq_s)$ and a nilpotent element of type $(1^{q_1-q_2},2^{q_2-q_3},\dots,(l-1)^{q_{l-1}-q_l},l^{q_l})$ by using the coproduct and evaluation map for the affine Yangian and the Miura map for non-rectangular $W$-algebras. As an application, we give a homomorphism from the affine Yangian to some cosets of non-rectangular $W$-algebras.
Submission history
From: Mamoru Ueda [view email][v1] Sun, 28 Apr 2024 04:03:18 GMT (15kb)
[v2] Sat, 4 May 2024 03:03:22 GMT (15kb)
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