Related papers: Modular reduction of the Steinberg lattice of the …
We study the Steinberg lattice of the general linear group when reduced modulo a prime different from the defining characteristic.
We define a certain compactifiction of the general linear group and give a modular description for its points with values in arbitrary schemes. This is a first step in the construction of a higher rank generalization of Gieseker's…
In this paper we study the general group classification of systems of linear second-order ordinary differential equations inspired from earlier works and recent results on the group classification of such systems. Some interesting results…
We study the construction of a modular generalized Springer correspondence for a possibly disconnected complex reductive algebraic group.
We completely determine all lower-modular elements of the lattice of all semigroup varieties. As a corollary, we show that a lower-modular element of this lattice is modular.
In this article we study the behavior of inertia groups for modular Galois mod l^n representations and in some cases we give a generalization of Ribet's lowering the level result
We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…
The notion of singular reduction modules, i.e., of singular modules of nonclassical (conditional) symmetry, of differential equations is introduced. It is shown that the derivation of nonclassical symmetries for differential equations can…
The Steinberg tensor product theorem is a fundamental result in the modular representation theory of reductive algebraic groups. It describes any finite-dimensional simple module of highest weight $\lambda$ over such a group as the tensor…
This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…
Given a connected reductive algebraic group G, we investigate the Picard group of the moduli stack of principal G-bundles over an arbitrary family of smooth curves.
Quantum hamiltonian reduction is a fundamental tool of conformal field theory and vertex algebra representation theory. It has traditionally been applied to study highest-weight modules. On the other hand, inverse quantum hamiltonian…
In this paper, we give a simple formula for sectional curvatures on the general linear group, which is also valid for many other matrix groups. Similar formula is given for a reductive Lie group. We also discuss the relation between…
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…
Reductions of N-wave type equations related to simple Lie algebras and the hierarchy of their Hamiltonian structures are studied. The reduction group G_R is realized as a subgroup of the Weyl group of the corresponding algebra. Some of the…
We prove that the isomorphism problem for group algebras reduces to group algebras over finite extensions of the prime field. In particular, the modular isomorphism problem reduces to finite modular group algebras.
We study reduction of generalized complex structures. More precisely, we investigate the following question. Let $J$ be a generalized complex structure on a manifold $M$, which admits an action of a Lie group $G$ preserving $J$. Assume that…
The aim of this paper is to present an explicit reduction algorithm for Hilbert modular groups over arbitrary totally real number fields. An implementation of the algorithm is available to download from [19]. The exposition is…
We introduce the modular class of a Poisson map. We look at several examples and we use the modular classes of Poisson maps to study the behavior of the modular class of a Poisson manifold under different kinds of reduction. We also discuss…
Twisted modules over vertex algebras formalize the relations among twisted vertex operators and have applications to conformal field theory and representation theory. A recent generalization, called twisted logarithmic module, involves the…