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A geometric realization of spin representations and Young diagrams from quiver varieties

2003/07/31 by Alistair Savage
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.AG #math.RT #msc:16G20 #msc:17B10

paper · pdf · doi:10.1016/j.jalgebra.2005.10.036

published as J. Algebra 297 (2006), no. 1, 186-207 · 21 pages, 9 figures; v2: Minor Corrections

arxiv created 2004/07/07 · openalex publication_date 2005/12/16 · arxiv updated 2012/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

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.

Citations