Related papers: Notes on partial conjugation
Recently, the concept of generalized partial-slice monogenic (or regular) functions has been introduced and studied over Clifford algebras and octonions, respectively. In this paper, we further develop the theory of generalized…
We present an averaging process for sections of a torsor under a unipotent group. This process allows one to integrate local sections of such a torsor into a global simplicial section. The results of this paper have applications to…
In this paper, we consider the diagonal action of a connected semisimple group of adjoint type on its wonderful compactification. We show that the semi-stable locus is a union of the $G$-stable pieces and we calculate the geometric…
The aim of this work is to prove a conjecture related to the Combinatorial Invariance Conjecture of Kazhdan-Lusztig polynomials, in the parabolic setting, for lower intervals in every arbitrary Coxeter group. This result improves and…
In this paper we consider Deligne-Lusztig varieties and their analogues when the Frobenius endomorphism is replaced with conjugation by an element in a group, especially a regular semisimple or regular unipotent one. We calculate their…
We define the notion of a partial action on a generalized Boolean algebra and associate to every such system and commutative unital ring $R$ an $R$-algebra. We prove that every strongly $E^{\ast}$-unitary inverse semigroup has an associated…
We study the cohomology of parabolic Deligne-Lusztig varieties associated to unipotent blocks of GLn(q). We show that the geometric version of Brou\'e's conjecture over Q_\ell, together with Craven's formula, holds for any unipotent block…
For unramified reductive groups, we determine the connected components of affine Deligne-Lusztig varieties in the partial affine flag varieties. Based on the work of Hamacher-Kim and Zhou, this result allows us to verify, in the unramified…
A generalization of G-sets, called partial G-sets, are the sets that admit an action of partial maps on their subsets. Partial actions are a powerful tool to generalize many results of group actions. These generalizations are obtained by…
For a given inverse semigroup S , we introduce the notion of algebraic crossed product by using a given partial action of S, and we will prove that under some condition it is associative. Also we will introduce the concept of partial…
Motivated by the desire to understand the geometry of the basic loci in the reduction of Shimura varieties, we study their "group-theoretic models" -- generalized affine Deligne-Lusztig varieties -- in cases where they have a particularly…
Fundamentals on Lie group methods and applications to differential equations are surveyed. Many examples are included to elucidate their extensive applicability for analytically solving both ordinary and partial differential equations.
We give a new proof of the fact that affine Deligne-Lusztig varieties for an algebraic group of adjoint type, associated with superbasic elements, are of finite type. The proof uses a property of the associated Hecke algebra, which we…
In this note we give some new results concerning the subgroup commutativity degree of a finite group $G$. These are obtained by considering the minimum of subgroup commutativity degrees of all sections of $G$.
We will construct the Lusztig form for the quantum loop algebra of $\mathfrak{gl}_n$ by proving the conjecture \cite[3.8.6]{DDF} and establish partially the Schur--Weyl duality at the integral level in this case. We will also investigate…
In this paper, we characterize suitable partial (co)actions of Taft and Nichols Hopf algebras on algebras, and moreover we get that such partial (co)actions are symmetric. For certain algebras, these partial (co)actions obtained are,…
In this paper we study the geometric structure of affine Deligne-Lusztig varieties for $GL_n$ and $b$ basic. We introduce a new condition on $\lambda$. If this is satisfied, then the corresponding affine Deligne-Lusztig variety is the…
Given an action of an affine algebraic group with only trivial characters on a factorial variety, we ask for categorical quotients. We characterize existence in the category of algebraic varieties. Moreover, allowing constructible sets as…
We investigate criteria for algebra extensions that are of Galois type with respect to the coaction of a Hopf algebra or, more generally, a one-sided quotient of a Hopf algebra, or with respect to an entwining. We study the module- and…
In a previous paper {GN2} an effective solution of the lattice point counting problem in general domains in semisimple S-algebraic groups and affine symmetric varieties was established. The method relies on the mean ergodic theorem for the…