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Communication Dans Un Congrès Année : 2019

Polynomial link invariants and quantum algebras

Résumé

The definition of the Jones polynomial in the 80's gave rise to a large family of so-called quantum link invariants, based on quantum groups. These quantum invariants are all controlled by the same two-variable invariant (the HOMFLY-PT polynomial), which also specializes to the older Alexander polynomial. Building upon quantum Schur--Weyl duality and variants of this phenomenon, I will explain an algebraic setup that allows for global definitions of these quantum polynomials, and discuss extensions of these quantum objects designed to encompass all of the mentioned invariants, including the HOMFLY-PT polynomial.

Dates et versions

hal-03203616 , version 1 (20-04-2021)

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Hoel Queffelec. Polynomial link invariants and quantum algebras. Winter Braids IX, Mar 2019, Reims, France. ⟨hal-03203616⟩
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