Let G be a classical group over an algebraically closed field of characteristic 2 and let C be an elliptic conjugacy class in the Weyl group. In a previous paper the first named author associated to C a unipotent conjugacy class Φ(C) of G. In this paper we show that Φ(C) can be characterized in terms of the closure relations between unipotent classes. Previously, the analogous result was known ...

This paper deals with generalized hypergeometric differential equations of order n ≥ 3 having maximal unipotent monodromy at 0. We show that, among these equations, those leading to mirror maps with integral Taylor coefficients at 0 (up to simple rescaling) have special parameters, namely R-partitioned parameters. This result yields the classification of all generalized hypergeometric different...

We give several explicit examples of quantum cluster algebra structures, as introduced by Berenstein and Zelevinsky, on quantized coordinate rings of partial flag varieties and their associated unipotent radicals. These structures are shown to be quantizations of the cluster algebra structures found on the corresponding classical objects by Geiß, Leclerc and Schröer, whose work generalizes that...

Let G be a classical group over an algebraically closed field of characteristic 2 and let C be an elliptic conjugacy class in the Weyl group. In a previous paper the first named author associated to C a unipotent conjugacy class Φ(C) of G. In this paper we show that Φ(C) can be characterized in terms of the closure relations between unipotent classes. Previously, the analogous result was known ...

An element $u$ of a ring $R$ is called \textsl{unipotent} if $u-1$ is
 nilpotent. Two elements $a,b\in R$ are \textsl{unipotent equivalent}
 there exist unipotents $p,q\in such that $b=q^{-1}ap$. square
 matrices $A,B$ \textsl{strongly unipotent equivalent} there
 triangular $P,Q$ with $B=Q^{-1}AP$.
 In this paper, over commutative reduced rings, we characterize the mat...

an algebraic construction for constant dimension subspace codes is called orbit code. it arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. in particular orbit codes of a singer subgroup of the general linear group has investigated recently. in this paper, we consider the normalizer of a singer subgroup of the general linear group a...

We develop a theory of microlocalization for Harish-Chandra modules, adapting construction Losev [Duke Math. J. 159 (2011), pp. 99–143]. explore the applications this to unipotent representations real reductive groups. For representation complex group, we deduce formula restriction maximal compact subgroup, proving an old conjecture Vogan [Associated varieities and representations</ital...

suppose $g$ is a split connected‎ ‎reductive orthogonal or symplectic group over an infinite field‎ ‎$f,$ $p=mn$ is a maximal parabolic subgroup of $g,$ $frak{n}$ is‎ ‎the lie algebra of the unipotent radical $n.$ under the adjoint‎ ‎action of its stabilizer in $m,$ every maximal prehomogeneous‎ ‎subspaces of $frak{n}$ is determined‎.