相关论文: Quivers of type A, flag varieties and representati…

We introduce the notion of (twisted) quiver representations in abelian categories and study the category of such representations. We construct standard resolutions and coresolutions of quiver representations and study basic homological…

Recent articles have shown the connection between representation theory of quivers and the theory of cluster algebras. In this article, we prove that some cluster algebras of type ADE can be recovered from the data of the corresponding…

These are lecture notes that arose from a representation theory course given by the first author to the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students,…

This is a survey paper of the theory of crystal bases, global bases and the cluster algebra structure on the quantum coordinate rings.

We give a brief introduction to (upper) cluster algebras and their quantization using examples. Then we present several important families of bases for these algebras using topological models. We also discuss tropical properties of these…

This note being devoted to some aspects of the inverse problem of representation theory contains a new insight into it illustrated by two topics. The attention is concentrated on the manner of representation of abstract objects by the…

This is a review paper on the algebraic structure and representations of the A type Yangian and the B, C, D types twisted Yangians. Some applications to constructions of Casimir elements and characteristic identities for the corresponding…

The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…

We construct a representation of the blob algebra over a ring allowing base change to every interesting (i.e. non--semisimple) specialisation which, in quasihereditary specialisations, passes to a full tilting module.

We survey some results on counting the rational points of moduli spaces of quiver representations. We then make generalizations to Grassmannians and flags of quiver representations. These results have nice applications to the cluster…

In this note devoted to some aspects of the inverse problem of representation theory the attention is concentrated on the interrelations between various algebraic structures (algebras with operators) unraveled by different solutions of the…

Let $G$ be a split semisimple linear algebraic group over a field and let $X$ be a generic twisted flag variety of $G$. Extending the Hilbert basis techniques to Laurent polynomials over integers we give an explicit presentation of the…

The connections amongst (1) quivers whose representation varieties are Calabi-Yau, (2) the combinatorics of bipartite graphs on Riemann surfaces, and (3) the geometry of mirror symmetry have engendered a rich subject at whose heart is the…

Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…

Improvements in the exposition.

We gave a classification of P and Q with a finite number of K-orbits of a double flag variety G/P*K/Q for a symmetric pair (G, K) when G=GL_{m+n} and K=GL_{m}*GL_{n}, and a description of K-orbits when the number of K-orbits of G/P*K/Q is…

A subvariety of a complex projective space has a well-known dual variety, which is the set of its tangent hyperplanes. The purpose of this paper is to generalise this notion for a subvariety of a quite general partial flag variety. A…

Theory of representations of F-algebra is a natural development of the theory of F-algebra. Exploring of morphisms of the representation leads to the concepts of generating set and basis of representation. In the book I considered the…

This is an expository paper which has two parts. In the first part, we study quiver varieties of affine $A$-type from a combinatorial point of view. We present a combinatorial method for obtaining a closed formula for the generating…

For a path algebra $A$ over a quiver $Q$, there are bijections between the support-tilting modules of $A$, torsion classes in $\mathrm{mod}(A)$ and wide subcategories in $\mathrm{mod}(A)$; these are part of the Ingalls-Thomas bijections. As…