Zobrazeno 1 - 10
of 206
pro vyhledávání: '"Brundan, Jonathan"'
We introduce a new family of monoidal categories which are cyclotomic quotients of the nil-Brauer category. We construct a monoidal functor from the cyclotomic nil-Brauer category to another monoidal category constructed from singular Soergel bimodul
Externí odkaz:
http://arxiv.org/abs/2410.15167
Autor:
Brundan, Jonathan
The $q$-Schur category is a $\mathbb{Z}[q,q^{-1}]$-linear monoidal category closely related to the $q$-Schur algebra. We explain how to construct it from coordinate algebras of quantum $GL_n$ for all $n \geq 0$. Then we use Donkin's work on Ringel du
Externí odkaz:
http://arxiv.org/abs/2407.07228
We prove that the Grothendieck ring of the monoidal category of finitely generated graded projective modules for the nil-Brauer category is isomorphic to an integral form of the split $\imath$-quantum group of rank one. Under this isomorphism, the in
Externí odkaz:
http://arxiv.org/abs/2305.05877
Autor:
Brundan, Jonathan
This article develops a practical technique for studying representations of $\Bbbk$-linear categories arising in the categorification of quantum groups. We work in terms of locally unital algebras which are $\mathbb{Z}$-graded with graded pieces that
Externí odkaz:
http://arxiv.org/abs/2305.05122
Publikováno v:
Ann. Rep. Theory 1 (2024), 21-58
We introduce the nil-Brauer category and prove a basis theorem for its morphism spaces. This basis theorem is an essential ingredient required to prove that nil-Brauer categorifies the split $\imath$-quantum group of rank one. As this $\imath$-quantu
Externí odkaz:
http://arxiv.org/abs/2305.03876
We prove odd analogs of results of Chuang and Rouquier on sl(2)-categorification. Combined also with recent work of the second author with Livesey, this allows us to complete the proof of Brou\'e's Abelian Defect Conjecture for the double covers of s
Externí odkaz:
http://arxiv.org/abs/2203.14149
Autor:
Brundan, Jonathan, Vargas, Max
Publikováno v:
J. Algebra 601 (2022), 198-279
We explain a new approach to the representation theory of the partition category based on a reformulation of the definition of the Jucys-Murphy elements introduced originally by Halverson and Ram and developed further by Enyang. Our reformulation inv
Externí odkaz:
http://arxiv.org/abs/2107.05099