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arXiv · 2005.01154

Polynomial ring representations of endomorphisms of exterior powers

Ommolbanin Behzad·Andre Contiero·Letterio Gatto·Renato Vidal Martins
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Abstract

A polynomial ring with rational coefficients is an irreducible representation of Lie algebras of endomorphisms of exterior powers of a infinite countable dimensional $\mathbb{Q}$-vector space. We give an explicit description of it, using suitable vertex operators on exterior algebras, which mimick those occurring in the bosonic vertex representation of the Lie algebra $gl_\infty$, due to Date--Jimbo--Kashiwara and Miwa (DJKM).

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Ommolbanin Behzad, Andre Contiero, Letterio Gatto, Renato Vidal Martins. 2020-05-03. Polynomial ring representations of endomorphisms of exterior powers. https://arxiv.org/abs/2005.01154

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