Browsing by Author "Elias, Ben"

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A Categorification of the Positive Half of Quantum sl3 at a Prime Root of Unity

Stephens, Andrew (University of Oregon, 2019-04-30)

We place a differential on $\dot\UC_{\mathfrak{sl}_3}^+$ and show that $\dot\UC_{\mathfrak{sl}_3}^+$ is Fc-filtered. This gives a categorification of the positive half of quantum $\sl_3$ at a prime root of unity.
A SPECIAL ENDOMORPHISM OF THE STANDARD GAITSGORY CENTRAL OBJECT OF THE AFFINE HECKE CATEGORY

Hathaway, Jay (University of Oregon, 2024-03-25)

Using the combinatorial description of the standard Gaitsgory centralobject of the (extended, graded) affine type A Hecke category due to Elias, we show the existence of and explicitly describe the unique endomorphism that ...
Diagrammatic Representation Theory of the Rank Two Symplectic Group

Bodish, Elijah (University of Oregon, 2022-10-04)

We study the diagrammatic representation theory of the group $Sp_4$ and the quantum group $U_q(\mathfrak{sp}_4)$, expanding on the previous results of Kuperberg about type $B_2= C_2$ webs. In particular, we construct a ...
Extending Higher Bruhat Orders to Non-longest Words in S_n

Hothem, Daniel (University of Oregon, 2021-09-13)

In this paper, we extend Manin and Schechtman's higher Bruhat orders for the symmetric group to higher Bruhat orders for non-longest words w in the symmetric group. We prove that the higher Bruhat orders of non-longest ...