Dualities for spin representations

2020/05/22 by Wenzl, Hans · 1 citation
#17B37 (primary) 17B10 #18M20 (secondary #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2005.11299

Abstract

Let S be the spinor representation of U_q\mathfrakso_N, for N odd and q² not a rooot of unity. We show that the commutant of its action on S^{⊗ n} is given by a representation of the nonstandard quantum group U'_-q²\mathfrakso_n. For N even, an analogous statement also holds for S=S₊⊕ S_- the direct sum of the irreducible spinor representations of U'_q\mathfrakso_N, with the commutant given by U'_-q\mathfrako_n, a ℤ/2-extension of U'_-q\mathfrakso_n. Similar statements also hold for fusion tensor categories with q a root of unity.

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