Related papers: Category $\mathcal{O}$ and asymptotic characters

We compute quantum character varieties of arbitrary closed surfaces with boundaries and marked points. These are categorical invariants $\int_S\mathcal A$ of a surface $S$, determined by the choice of a braided tensor category $\mathcal A$,…

We study asymptotics of integrals of certain rational functions that depend on parameters in a field $K$ of characteristic zero. We use formal power series to represent the integral and prove certain identities about its coefficients…

Generalizing Lusztig's work, Malle has associated to some imprimitive complex reflection group $W$ a set of "unipotent characters", which are in bijection of the usual unipotent characters of the associated finite reductive group if $W$ is…

In this paper we give an asymptotic formula for a matrix integral which plays a crucial role in the approach of Diaconis et al. to random matrix eigenvalues. The choice of parameter for the asymptotic analysis is motivated by an invariant…

In this paper, we continue the development of a new combinatorial model for the irreducible characters of a complex semisimple Lie group. This model, which will be referred to as the alcove path model, can be viewed as a discrete…

The Chern character maps are one of the most important working tools in mathematics. Although they admit numerous different constructions, they are not yet fully understood at the conceptual level. In this note we eliminate this gap by…

Let $(G,\kappa)$ be a compact connected Lie group endowed with a biinvariant Riemannian metric, and let $\tilde{G}$ be the complexification of $G$. We apply Grauert tube techniques to the near-diagonal scaling asymptotics of certain…

In this paper, we extend the Topological Quantum Field Theory developed by Gonz\'alez-Prieto, Logares, and Mu\~noz for computing virtual classes of $G$-representation varieties of closed orientable surfaces in the Grothendieck ring of…

In 2015, Lusztig [Bull. Inst. Math. Acad. Sin. (N.S.)10(2015), no.1, 1-72] showed that for a connected reductive group over an algebraic closure of a finite field the associated (geometric) Hecke category admits a truncation in a two-sided…

Let $G$ be a connected reductive algebraic group over an algebraically closed field of positive characteristic, $\mathfrak{g}$ be its Lie algebra, and $B$ be a Borel subgroup. We prove a formula for the dimensions of extension groups, in…

We construct a family of infinite-dimensional positive sub-coalgebras within the Grothendieck ring of Hecke algebras, when viewed as a Hopf algebra with respect to the induction and restriction functor. These sub-coalgebras have as…

We consider the algebraic K-theory of a truncated polynomial algebra in several commuting variables, K(k[x_1, ..., x_n]/(x_1^a_1, ..., x_n^a_n)). This naturally leads to a new generalization of the big Witt vectors. If k is a perfect field…

We develop the theory of a category ${\mathscr C}_A$ which is a generalisation to non-restricted ${\mathfrak g}$-modules of a category famously studied by Andersen, Jantzen and Soergel for restricted ${\mathfrak g}$-modules, where…

The characteristic map for the symmetric group is an isomorphism relating the representation theory of the symmetric group to symmetric functions. An analogous isomorphism is constructed for the symmetric space of symplectic forms over a…

Jack characters are a one-parameter deformation of the characters of the symmetric groups; a deformation given by the coefficients in the expansion of Jack symmetric functions in the basis of power-sum symmetric functions. We study Jack…

We provide a linkage principle in an arbitrary parabolic category $\mathcal O^{\mathfrak p}$ for the periplectic Lie superalgebras $\mathfrak{pe}(n)$. As an application, we classify indecomposable blocks in $\mathcal O^{\mathfrak p}$. We…

We argue for the addition of category theory to the toolkit of toric topology, by surveying recent examples and applications. Our case is made in terms of toric spaces X_K, such as moment-angle complexes Z_K, quasitoric manifolds M, and…

Let $k$ be a field of characteristic zero containing all roots of unity and $K=k((t))$. We build a ring morphism from the Grothendieck group of semi-algebraic sets over $K$ to the Grothendieck group of motives of rigid analytic varieties…

The homogeneous coordinate ring $\mathbb{C}[\operatorname{Gr}(k,n)]$ of the Grassmannian is a cluster algebra, with an additive categorification $\operatorname{CM}C$. Thus every $M\in\operatorname{CM}C$ has a cluster character…

Let k be any field. J-P. Serre proved that the spectrum of the Grothendieck ring of the k-representation category of a group is connected, and that the same holds in characteristic zero for the representation category of a Lie algebra over…