Related papers: q-Schur algebras and quantum Frobenius
We construct a family of graded isomorphisms between certain subquotients of diagrammatic Cherednik algebras as the quantum characteristic, multicharge, level, degree, and weighting are allowed to vary; this provides new structural…
A construction of the quantum affine algebra $U_q(g)$ is given in two steps. We explain how to obtain the algebra from its positive Borel subalgebra $U_q(b^+)$, using a construction similar to Drinfeld's quantum double. Then we show how the…
We construct a PROP which encodes 2D-TQFTs with a grading. This defines a graded Frobenius algebra as algebras over this PROP. We also give a description of graded Frobenius algebras in terms of maps and relations. This structure naturally…
We determine explicit quantum seeds for classes of quantized matrix algebras. Furthermore, we obtain results on centers and block diagonal forms {of these algebras.} In the case where $q$ is {an arbitrary} root of unity, this further…
We formulate a $q$-Schur algebra associated to an arbitrary $W$-invariant finite set $X_{\texttt f}$ of integral weights for a complex simple Lie algebra with Weyl group $W$. We establish a $q$-Schur duality between the $q$-Schur algebra…
Derived equivalences for Artin algebras (and almost $\nu$-stable derived equivalences for finite-dimensional algebras) are constructed from Milnor squares of algebras. Particularly, three operations of gluing vertices, unifying arrows and…
We give closed formulae for the q-characters of the fundamental representations of the quantum loop algebra of a classical Lie algebra in terms of a family of partitions satisfying some simple properties. We also give the multiplicities of…
This is a survey of what is known and/or conjectured about the prime and primitive spectra of quantum algebras, of quantized coordinate rings in particular. The topological structure of these spectra, their relations to classical affine…
We study Frobenius-Schur indicators of the regular representations of finite-dimensional semisimple Hopf algebras, especially group-theoretical ones. Those of various Hopf algebras are computed explicitly. In view of our computational…
The affine quantum Schur algebra is a certain important infinite dimensional algebra whose representation theory is closely related to that of quantum affine $\frak{gl}_n$. Finite dimensional irreducible modules for the affine quantum Schur…
We describe a connection between finite--dimensional representations of quantum affine algebras and affine Hecke algebras.
To each symmetric graded Frobenius superalgebra we associate a W-algebra. We then define a linear isomorphism between the trace of the Frobenius Heisenberg category and a central reduction of this W-algebra. We conjecture that this is an…
In \cite{DFW} and \cite{Fu07}, little $q$-Schur algebras were introduced as homomorphic images of the infinitesimal quantum groups. In this paper, we will investigate representations of these algebras. We will classify simple modules for…
We develop a graded version of the theory of cyclotomic q-Schur algebras, in the spirit of the work of Brundan-Kleshchev on Hecke algebras and of Ariki on q-Schur algebras. As an application, we identify the coefficients of the canonical…
An important breakthrough in understanding the geometry of Schubert varieties was the introduction of the notion of Frobenius split varieties and the result that the flag varieties G/P are Frobenius split. The aim of this article is to give…
Lusztig has constructed a Frobenius morphism for quantum groups at an $\ell$-th root of unity, which gives an integral lift of the Frobenius map on universal enveloping algebras in positive characteristic. Using the Hall algebra we give a…
We give a presentation of cyclotomic q-Schur algebras by generators and defining relations. As an application, we give an algorithm for computing decomposition numbers of cyclotomic q-Schur algebras.
We consider various specializations of the non-twisted quantum affine algebras at roots of unity. We define and study the q-characters of their finite-dimensional representations.
We define a class of quantum linear Galois algebras which include the universal enveloping algebra Uq(gln), the quantum Heisenberg Lie algebra and other quantum orthogonal Gelfand-Zetlin algebras of type A, the subalgebras of G-invariants…
Building up on our previous works regarding $q$-deformed $P$-partitions, we introduce a new family of subalgebras for the ring of quasisymmetric functions. Each of these subalgebras admits as a basis a $q$-analogue to Gessel's fundamental…