Infinite rank spinor and oscillator representations

  • Steven V Sam

    University of Wisconsin, Madison, USA
  • Andrew Snowden

    University of Michigan, Ann Arbor, USA

Abstract

We develop a functorial theory of spinor and oscillator representations parallel to the theory of Schur functors for general linear groups. This continues our work on developing orthogonal and symplectic analogues of Schur functors. As such, there are a few main points in common. We define a category of representations of what might be thought of as the infinite rank pin and metaplectic groups, and give three models of this category in terms of: multilinear algebra, diagram categories, and twisted Lie algebras. We also define specialization functors to the finite rank groups and calculate the derived functors.

Cite this article

Steven V Sam, Andrew Snowden, Infinite rank spinor and oscillator representations. J. Comb. Algebra 1 (2017), no. 2, pp. 145–183

DOI 10.4171/JCA/1-2-2