Cellular structures using U_q-tilting modules
read the original abstract
We use the theory of $\textbf{U}_q$-tilting modules to construct cellular bases for centralizer algebras. Our methods are quite general and work for any quantum group $\textbf{U}_q$ attached to a Cartan matrix and include the non-semisimple cases for $q$ being a root of unity and ground fields of positive characteristic. Our approach also generalizes to certain categories containing infinite-dimensional modules. As applications, we give a new semisimplicty criterion for centralizer algebras, and recover the cellularity of several known algebras (with partially new cellular bases) which all fit into our general setup.
This paper has not been read by Pith yet.
Forward citations
Cited by 4 Pith papers
-
On a symplectic quantum Howe duality
Proves nonsemisimple quantum Howe duality for Sp(2n) and SL(2) on exterior algebra of type C, with character formulas and canonical bases.
-
On Hecke and asymptotic categories for a family of complex reflection groups
Constructs Hecke algebras and asymptotic versions for G(M,M,N) complex reflection groups by generalizing the dihedral case.
-
Growth problems in diagram categories
Derives asymptotic formulas for the growth rate of the number of summands in tensor powers of the generating object in semisimple diagram/interpolation categories.
-
Orthogonal webs and semisimplification
A diagrammatic category equivalent to tilting representations of the orthogonal group is defined and its semisimplification is described, valid in characteristic not equal to two.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.