Related papers: Quivers of type A, flag varieties and representati…
We consider representation spaces of quivers, together with their base change action, and classify the spherical varieties among them.
This is an expanded version of lectures given at a Summer School "Geometric methods in Representation Theory" (Grenoble, 2008).
Our concern in this paper is the dimension and inclusion relations of Schubert varieties in twisted partial affine flag varieties. In the end we apply our results to some local models of certain Schubert varieties.
We systematically determine the regular representations, quivers and representation type of all liftings of two-dimensional quantum linear spaces.
We give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.
In this brief expository article we review the background for biquandle bracket quivers -- including biquandles, biquandle homsets, biquandle coloring quivers and biquandle brackets -- for a talk at the 70th Topology Symposium at Nara…
These notes reflect the contents of three lectures given at the workshop of the 14th International Conference on Representations of Algebras (ICRA XIV), held in August 2010 in Tokyo. We first provide an introduction to quantum loop algebras…
We study the representation theory of the nested instantons quiver presented in [1], which describes a particular class of surface defects in four-dimensional supersymmetric gauge theories. We show that the moduli space of its stable…
We describe the "generic" part of the character ring of general linear groups over a finite field in terms of quiver representations.
For any semifield K we define a K-form of a partial flag manifold of a semisimple group G of simply laced type over the complex numbers. The definition is in terms of the theory of canonical bases.
The paper surveys various Waring type problems in groups, Lie algebras, and associative algebras.
This is a brief overview of a few selected chapters on automorphism groups of affine varieties. It includes some open questions.
We give a presentation of the torus-equivariant quantum $K$-theory ring of flag manifolds of type $A$, as a quotient of a polynomial ring by an explicit ideal. This is the torus-equivariant version of our previous result, which gives a…
We define quantum equivariant K-theory of Nakajima quiver varieties. We discuss type A in detail as well as its connections with quantum XXZ spin chains and trigonometric Ruijsenaars-Schneider models. Finally we study a limit which produces…
Quiver Grassmannians are varieties parametrizing subrepresentations of a quiver representation. It is observed that certain quiver Grassmannians for type A quivers are isomorphic to the degenerate flag varieties investigated earlier by the…
These are notes from my mini-course at ICRA13, Sao Paulo, 2008
ICM lecture on minimal models and moduli of varieties.
Survey article on the geometry of spherical varieties. Invited survey for Transformation Groups.
We introduce quiver gauge theory associated with the non-simply-laced type fractional quiver, and define fractional quiver W-algebras by using construction of arXiv:1512.08533 and arXiv:1608.04651 with representation of fractional quivers.
This text is devoted to the theory of varieties, which provides an important tool, based in universal algebra, for the classification of regular languages. In the introductory section, we present a number of examples that illustrate and…