Related papers: Modular generalized Springer correspondence I: the…
This paper is a survey on the topics concerning the Springer correspondence related to the varieties such as the enhanced variety or the exotic symmetric space. We explain in the case of exotic symmetric space of higher level, the complex…
Generalized complex geometry is a new mathematical framework that is useful for describing the target space of N=(2,2) nonlinear sigma-models. The most direct relation is obtained at the N=(1,1) level when the sigma model is formulated with…
We develop representation theory of general linear groups in the category $\text{Ver}_4^+$, the simplest tensor category which is not Frobenius exact. Since $\text{Ver}_4^+$ is a reduction of the category of supervector spaces to…
In this note we give a self-contained proof of the following classification (up to conjugation) of subgroups of the general symplectic group of dimension n over a finite field of characteristic l, for l at least 5, which can be derived from…
We develop a theory of general sheaves over weighted projective lines. We define and study a canonical decomposition, analogous to Kac's canonical decomposition for representations of quivers, study subsheaves of a general sheaf, general…
We introduce a class of perverse sheaves on a partial flag manifold of a connected reductive group G defined over a finite field which are equivariant under the action of the group of rational points of G. The definition of this class is…
We classify indecomposable summands of mixed tensor powers of the natural representation for the general linear supergroup up to isomorphism. We also give a formula for the characters of these summands in terms of composite supersymmetric…
Given a semisimple element in the loop Lie algebra of a reductive group, we construct a quasi-coherent sheaf on a partial resolution of the trigonometric commuting variety of the Langlands dual group. The construction uses affine Springer…
A well-known conjecture says that every one-relator group is coherent. We state and partly prove an analogous statement for graded associative algebras. In particular, we show that every Gorenstein algebra $A$ of global dimension 2 is…
We investigate a version of the Green correspondence for categories of complexes, including homotopy categories and derived categories. The correspondence is an equivalence between a category defined over a finite group $G$ and the same for…
We show a correspondence between tensor representations of the super general linear group GL(m|n) and tensor representations of the general linear superalgebra gl(m|n) constructed by Berele and Regev.
Given a closed, oriented surface X of genus g>1, and a semisimple Lie group G, let R_G be the moduli space of reductive representations of the fundamental group of X in G. We determine the number of connected components of R_PGL(n,R), for…
Generalized Halphen systems are solved in terms of functions that uniformize genus zero Riemann surfaces, with automorphism groups that are commensurable with the modular group. Rational maps relating these functions imply subgroup…
We study certain correspondences over Drinfeld modular varieties given by sums of Hecke correspondences. We propose generalizations of Stickelberger's theorem for higher dimensions. Using this result, we study anihilators for some cusp…
Some sorts of generalized morphisms are defined from very basic mathematical objects such as sets, functions, and partial functions. A wide range of mathematical notions such as continuous functions between topological spaces, ring…
In this article, we study the modular representations of the special linear group of degree two over a finite field in defining characteristic. In particular, we study the automorphisms of derived category of representations. We have been…
We complete the determination of the generalised Springer correspondence for connected reductive algebraic groups, by proving a conjecture of Lusztig on the last open cases which occur for groups of type $E_8$.
Pursuing a generalization of group symmetries of modular categories to category symmetries in topological phases of matter, we study linear Hopf monads. The main goal is a generalization of extension and gauging group symmetries to category…
Consider the general linear group, which is not connected but rather has two connected components, the matrices with positive determinant and the ones with negative determinant. Consider the Iwasawa decomposition of its special linear…
We describe the generic modules in each component of the spaces of representations of certain string algebras. In so doing, we calculate the dimensions of higher self-extension groups for generic modules. This algorithm lends itself for use…