A new presentation and categorification of the osp(1|2)-link invariant

Date:

Time:

2023 01 23

15:30 (GMT+0)

Speaker:

Mark Ebert

Knots and representation theory

There is a known connection between the quantum osp(1|2n) and so(2n+1) polynomial knot invariants studied by Blumen and Clark.
In the rank 1 case, the uncolored U_q(osp(1|2)) invariant is equal to the U_{t^{-1}q}(sl_2) invariant where t^2=-1.
Blumen defined these invariants using Markov traces on Birman-Wenzl-Murakami algebras and Clark constructed the invariants using the representation theory of the quantum covering group.

In this talk, we construct a link invariant that coincides with Clark's uncolored osp(1|2) link invariant on oriented links.
This new presentation of the osp(1|2) link invariant is defined using a Kauffman bracket-type skein relation and Markov traces on the Temperley–Lieb algebra.
We construct this presentation of the osp(1|2) link invariant using the representation theory of the quantum covering group, and compare our construction to Clark's.
Finally, we categorify the osp(1|2)-invariant using a modified version of Khovanov homology equipped with an extra Z_4 -grading.

Time line

Chicago -8h

Moscow +0h

Beijing +5h

Seoul +6h

Tokyo +6h