Related papers: Finite Crystals and Paths

We construct a 2-category of differential graded schemes. The local affine models in this theory are differential graded algebras, which are graded commutative with unit over a field of characteristic zero, are concentrated in non-positive…

We achieve an extremely useful description (up to isomorphism) of the Leavitt path algebra $L_K(E)$ of a finite graph $E$ with coefficients in a field $K$ as a direct sum of matrix rings over $K$, direct sum with a corner of the Leavitt…

Given two convex polytopes, the join, the cartesian product and the direct sum of them are well understood. In this paper we extend these three kinds of products to abstract polytopes and introduce a new product, called the topological…

Indecomposible semifinite harmonic functions on the direct product of graded graphs are classified. As a particular case, the full list of indecomposible traces for the infinite inverse symmetric semigroup is obtained.

For a connected semisimple algebraic group $G$, we consider some special infinite series of tensor products of simple $G$-modules whose $G$-fixed point spaces are at most one-dimensional. We prove that their existence is closely related to…

Irreducible representations of both Leavitt and Cohn path algebras of an arbitrary digraph with coefficients in a commutative field is classified. They are constructed in several ways using both infinite paths on the right as well as direct…

For an interval finite quiver $Q$, we introduce a class of flat representations. We classify the indecomposable projective objects in the category $\mathrm{rep}(Q)$ of pointwise finite dimensional representations. We show that an object in…

Let $k$ be an infinite finitely generated field of characteristic $p>0$. Fix a separated scheme $X$ smooth, geometrically connected, and of finite type over $k$ and a smooth proper morphism $f:Y\rightarrow X$. The main result of this paper…

For an untwisted affine Lie algebra we prove an embedding of any higher level Demazure module into a tensor product of lower level Demazure modules (e.g. level one in type A) which becomes in the limit (for anti-dominant weights) the…

In this paper, we develop the crystal basis theory for the quantum queer superalgebra $\Uq$. We define the notion of crystal bases, describe the tensor product rule, and present the existence and uniqueness of crystal bases for…

We establish an explicit algebra isomorphism between the affine Yokonuma-Hecke algebra $\widehat{Y}_{r,n}(q)$ and a direct sum of matrix algebras with coefficients in tensor products of affine Hecke algebras of type $A.$ As an application…

A Littelmann path model is constructed for crystals pertaining to a not necessarily symmetrizable Borcherds-Cartan matrix. Here one must overcome several combinatorial problems coming from the imaginary simple roots. The main results are an…

Let Q be a finite quiver without oriented cycles. Denote by U --> M the fine moduli space of stable thin sincere representations of Q with respect to the canonical stability notion. We prove Ext^i(U,U) = 0 for all i >0 and compute the…

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…

Examples of simple, separable, unital, purely infinite $C^*$--algebras are constructed, including: (1) some that are not approximately divisible; (2) those that arise as crossed products of any of a certain class of $C^*$--algebras by any…

This paper contains three related groupings of results. First, we consider a new notion of an admissible skein module of a surface associated to an ideal in a (non-semisimple) pivotal category. Second, we introduce the notion of a chromatic…

We define an action of the braid group (associated with a simple Lie algebra) on the space of $n$-tuples of power series in an indeterminate u, with constant term zero. Using this, we give a sufficient condition for a tensor product of…

We investigate the interplay of crystal bases and completions in the sense of Enright on certain nonintegrable representations of quantum groups. We define completions of crystal bases, show that this notion of completion is compatible with…

We study quantum integrable models with $GL(3)$ trigonometric $R$-matrix solvable by the nested algebraic Bethe ansatz. We analyze scalar products of generic Bethe vectors and obtain an explicit representation for them in terms of a sum…

We study exact module categories over the representation categories of finite-dimensional quasi-Hopf algebras. As a consequence we classify exact module categories over some families of pointed tensor categories with cyclic group of…