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arXiv · 1712.00707

Feigin's map revisited

Changjian Fu
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Abstract

The aim of this note is to understand the injectivity of Feigin's map $\mathbf{F_w}$ by representation theory of quivers, where $\mathbf{w}$ is the word of a reduced expression of the longest element of a finite Weyl group. This is achieved by the Ringel-Hall algebra approach and a careful studying of a well-knwon total order on the category of finite-dimensional representations of a valued quiver of finite type. As a byproduct, we also generalize Reineke's construction of monomial bases to non-simply-laced cases.

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Changjian Fu. 2017-12-03. Feigin's map revisited. https://arxiv.org/abs/1712.00707

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