Mixed quantum skew Howe duality and link invariants of type A |
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Authors: | Hoel Queffelec Antonio Sartori |
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Affiliation: | 1. Institut Montpelliérain Alexander Grothendieck, CNRS, Univ. Montpellier, France |
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Abstract: | We define a ribbon category , depending on a parameter β, which encompasses Cautis, Kamnitzer and Morrison's spider category, and describes for the monoidal category of representations of generated by exterior powers of the vector representation and their duals. We identify this category with a direct limit of quotients of a dual idempotented quantum group , proving a mixed version of skew Howe duality in which exterior powers and their duals appear at the same time. We show that the category gives a unified natural setting for defining the colored link invariant (for ) and the colored HOMFLY-PT polynomial (for β generic). |
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Keywords: | 17B35 17B37 20G43 57M25 57M27 81R50 Webs Spider category Quantum Lie superalgebras Skew-Howe duality HOMFLY-PT polynomial Reshetikhin–Turaev invariants |
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