Journal of Combinatorial Algebra

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Volume 1, Issue 2, 2017, pp. 145–183
DOI: 10.4171/JCA/1-2-2

Published online: 2017-04-06

Infinite rank spinor and oscillator representations

Steven V Sam and Andrew Snowden[1]

(1) University of Michigan, Ann Arbor, USA

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.

Keywords: Spin representations, representation stability, invariant theory

Sam Steven V, Snowden Andrew: Infinite rank spinor and oscillator representations. J. Comb. Algebra 1 (2017), 145-183. doi: 10.4171/JCA/1-2-2