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arXiv · 1410.2932

Geometric Realizations of the Basic Representation of $\widehat\mathfrak{gl}_r$

Joel Lemay
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Abstract

The realizations of the basic representation of $\widehat\mathfrak{gl}_r$ are known to be parametrized by partitions of r and have an explicit description in terms of vertex operators on the bosonic/fermionic Fock space. In this paper, we give a geometric interpretation of these realizations in terms of geometric operators acting on the equivariant cohomology of certain Nakajima quiver varieties.

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Joel Lemay. 2014-10-11. Geometric Realizations of the Basic Representation of $\widehat\mathfrak{gl}_r$. https://arxiv.org/abs/1410.2932

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