相关论文: The algebra of Mirkovic-Vilonen cycles in type A

Kontsevich's formality theorem states that the differential graded Lie algebra of multidifferential operators on a manifold M is L-infinity-quasi-isomorphic to its cohomology. The construction of the L-infinity map is given in terms of…

We present a quantization of an isomorphism of Mirkovi\'c and Vybornov which relates the intersection of a Slodowy slice and a nilpotent orbit closure in $\mathfrak{gl}_N$ , to a slice between spherical Schubert varieties in the affine…

Let X be a complex manifold. The classical Riemann-Hilbert correspondence associates to a regular holonomic system M the C-constructible complex of its holomorphic solutions. Denote by t the affine coordinate in the complex projective line.…

We define and study the Drinfeld-Lafforgue-Vinberg compactification of the moduli stack of G-bundles Bun_G for an arbitrary reductive group G; its definition is given in terms of the Vinberg semigroup of G, and is due to Drinfeld…

For a commutative ring $A$, we have the category of (bounded-below) chain complexes of $A$-modules $Ch_{+}(A\mymod)$, a closed symmetric monoidal category with a compatible stable Quillen model structure. The associated homotopy category is…

The combinatorial description via ribbon graphs of the moduli space of Riemann surfaces makes it possible to define combinatorial cycles in a natural way. Witten and Kontsevich first conjectured that these classes are polynomials in the…

In this paper, a new algebraic structure is defined, which is a new MV-algebra that has a product operation, we will call it MVW-rig (Multivalued-weak rig). This structure is defined with universal algebra axioms, it is presented with a…

We define the associated variety $ X_{M} $ of a module $ M $ over a finite-dimensional superalgebra $ {\mathfrak g} $, and show how to extract information about $ M $ from these geometric data. $ X_{M} $ is a subvariety of the cone $ X $ of…

We give an explicit subword complex description of the generators of the type cone of the g-vector fan of a finite type cluster algebra with acyclic initial seed. This yields in particular a description of the Newton polytopes of the…

Gelfand's charecterization of a topological space M by the duality relationship of M and $\mathcal{A} = \mathcal{F}(M)$, the commutative algebra of functions on this space has deep implications including the development of spectral calculas…

In this paper we consider the category $C (\tilde k, \tilde H)$ of the $(\tilde k, \tilde H)$-modules, including all the Verma modules, where $k$ is some compact Lie algebra and H some Cartan subgroup, $\tilde k$ and $\tilde H$ are the…

This paper develops the basics of the theory of involutive categories and shows that such categories provide the natural setting in which to describe involutive monoids. It is shown how categories of Eilenberg-Moore algebras of involutive…

We introduce C-Algebras of compact Riemann surfaces $\Sigma$ as non-commutative analogues of the Poisson algebra of smooth functions on $\Sigma$. Representations of these algebras give rise to sequences of matrix-algebras for which…

Let $V$ be a complete discrete valuation ring with residue field $k$ and with fraction field $K$ of characteristic 0. We clarify the analysis behind the Monsky--Washnitzer completion of a commutative $V$-algebra using spectral radius…

Let A be the path algebra of a quiver Q with no oriented cycle. We study geometric properties of the Grassmannians of submodules of a given A-module M. In particular, we obtain some sufficient conditions for smoothness, polynomial…

Let G be a simply connected semisimple algebraic group over an algebraically closed field k of positive characteristic. We will untwist the structure of G-modules by a newly found splitting of the Frobenius endomorphism on the algebra of…

We construct an abelian category C and exact functors in C which on the Grothendieck group descend to the action of a simply-laced quantum group in its adjoint representation. The braid group action in the adjoint representation lifts to an…

Let $O$ be a closed Poisson conjugacy class of the complex algebraic Poisson group GL(n) relative to the Drinfeld-Jimbo factorizable classical r-matrix. Denote by $T$ the maximal torus of diagonal matrices in GL(n). With every $a\in O\cap…

Let $G$ be a complex classical group, and let $V$ be its defining representation (possibly plus a copy of the dual). A foundational problem in classical invariant theory is to write down generators and relations for the ring of…

Let K be a field of characteristic 2 and G a nonabelian locally finite 2-group. Let V(KG) be the group of units with augmentation 1 in the group algebra KG. An explicit list of groups is given, and it is proved that all involutions in V(KG)…