Related papers: The octahedron recurrence and gl(n) crystals

In 1991 V. Ginzburg observed that one can realize irreducible representations of the group $GL(n,C)$ in the cohomology of certain Springer's fibers for the group GL(d) (for all natural d). However, Ginzburg's construction of the action of…

We compare the (horizontal) trace of the affine Hecke category with the elliptic Hall algebra, thus obtaining an "affine" version of the construction of [14]. Explicitly, we show that the aforementioned trace is generated by the objects…

For each $n \in \mathbb{N} \cup \{\infty\}$, diagrammatic sets admit a model structure whose fibrant objects are the diagrammatic $(\infty, n)$- categories. They also support a notion of Gray product given by the Day convolution of a…

Let $G = G_{1} \times G_{2}$ be a product of two locally compact, second countable groups and $\mu \in \mathrm{Prob}(G)$ be of the form $\mu = \mu_{1} \times \mu_{2}$, where $\mu_{i} \in \mathrm{Prob}(G_{i})$. Let $(B,\nu_B)$ be the…

We define the notion of braided Coxeter category, which is informally a tensor category carrying compatible, commuting actions of a generalised braid group B_W and Artin's braid groups B_n on the tensor powers of its objects. The data which…

We show that under favorable circumstances, one can construct an intersection product on the Chow groups of a tensor triangulated category $\mathcal{T}$ (as defined by Balmer) which generalizes the usual intersection product on a…

A notion of stratification is introduced for any compactly generated triangulated category T endowed with an action of a graded commutative noetherian ring R. The utility of this notion is demonstrated by establishing diverse consequences…

In this paper we study properties of a homomorphism $\rho$ from the universal enveloping algebra $U=U(\mathfrak{gl}(n+1))$ to a tensor product of an algebra $\mathcal D'(n)$ of differential operators and $U(\mathfrak{gl}(n))$. We find a…

Let A be a Hopf algebra and H a coalgebra. We shall describe and classify up to an isomorphism all Hopf algebras E that factorize through A and H: that is E is a Hopf algebra such that A is a Hopf subalgebra of E, H is a subcoalgebra in E…

Let k be a field, q in k. We derive a cup product formula on the Hochschild cohomology ring of a family Lambda_q of quiver algebras. Using this formula, we determine a subalgebra of k[x,y] isomorphic to Hochschild cohomology modulo N, where…

We generalize the construction of reflection functors from classical representation theory of quivers to arbitrary small categories with freely attached sinks or sources. These reflection morphisms are shown to induce equivalences between…

We construct knot invariants categorifying the quantum knot variants for all representations of quantum groups. We show that these invariants coincide with previous invariants defined by Khovanov for sl_2 and sl_3 and by Mazorchuk-Stroppel…

We show that the braided tensor product algebra $A_1\underline{\otimes}A_2$ of two module algebras $A_1, A_2$ of a quasitriangular Hopf algebra $H$ is equal to the ordinary tensor product algebra of $A_1$ with a subalgebra of…

We compare the integral category O of shifted affine quantum groups of symmetric and non symmetric types. To do so we compute the K-theoretic analog of the Coulomb branches with symmetrizers introduced by Nakajima and Weekes. This yields an…

On the set H_n(K) of symmetric n by n matrices over the field K we can define various binary and ternary products which endow it with the structure of a Jordan algebra or a Lie or Jordan triple system. All these non-associative structures…

Given a commutative noetherian ring $R$ and a finite acyclic quiver $Q$, we study the tensor triangulated category $\mathcal{D}(RQ)$ endowed with the vertexwise tensor product. We find a description of the internal hom functor and show that…

We introduce (partially) ordered Grothendieck categories and apply results on their structure to the study of categories of representations of the Mackey Lie algebra of infinite matrices $\mathfrak{gl}^M\left(V,V_*\right)$. Here…

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…

We show that anyon chains, after stabilizing with infinite-dimensional ancilla spaces, factorize locally as tensor products of infinite-dimensional Hilbert spaces. This implies that any unitary fusion category can be realized as symmetries…

The Lascoux-Leclerc-Thibon-Ariki theory asserts that the K-group of the representations of the affine Hecke algebras of type A is isomorphic to the algebra of functions on the maximal unipotent subgroup of the group associated with a Lie…