A Geometric Realization of Spin Representations and Young diagrams from Quiver Varieties

Alistair Savage

doi:10.1016/j.jalgebra.2005.10.036

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A Geometric Realization of Spin Representations and Young diagrams from Quiver Varieties

Alistair Savage

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Abstract

Applying the techniques of an earlier paper with Frenkel, we develop a geometric realization of spin representations and Clifford algebras. In doing so, we give an explicit parametrization of the irreducible components of Nakajima varieties of type D in terms of Young diagrams. We explicity compute the geometric action of the Lie algebra and are able to extend the geometric action to the entire Clifford algebra used in the classical construction of the spin representations.

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Alistair Savage. 2004-07-07. A Geometric Realization of Spin Representations and Young diagrams from Quiver Varieties. https://doi.org/10.1016/j.jalgebra.2005.10.036

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