The purpose of this article is to study determinants of matrices which are known as generalized Pascal triangles (see [1]). We present a factorization by expressing such a matrix as a product of a unipotent lower triangular matrix, a Töeplitz matrix and a unipotent upper triangular matrix. The determinant of a generalized Pascal matrix equals thus the determinant of a Töeplitz matrix. This equa...

Finite simple, unipotent Bol loops have recently been identified and constructed using group theory. However, the purely group-theoretical constructions of the actual loops are indirect, somewhat arbitrary in places, and rely on computer calculations to a certain extent. In the spirit of revisionism, this paper is intended to give a more explicit combinatorial specification of the smallest simp...

Let W be a finite Weyl group and σ a non-trivial graph automorphism of W . We show a remarkable relation between the σ-twisted involution module for W and the Frobenius–Schur indicators of the unipotent characters of a corresponding twisted finite group of Lie type. This extends earlier results of Lusztig and Vogan for the untwisted case and then allows us to state a general result valid for an...

The main result of the current paper is a new parametrization of the orbits of a symmetric subgroup K on a partial flag variety P . The parametrization is in terms of certain Spaltenstein varieties, on one hand, and certain nilpotent orbits, on the other. One of our motivations, as explained below, is related to enumerating special unipotent representations of real reductive groups. Another mot...

Abstract We consider a special class of unipotent periods for automorphic forms on finite cover reductive adelic group $$\mathbf {G}(\mathbb {A}_\mathbb {K})$$ G ( A K ) , which we refer to as Fou...

We study Kakutani equivalence in the class of unipotent flows acting on finite-volume quotients semisimple Lie groups. For every such flow, we compute invariant M. Ratner, value being explicitly given by Jordan block structure element generating flow. This, particular, answers a question Ratner. Moreover, it follows that only loosely Kronecker are (1t 01)×id (SL(2,R)×G′)∕Γ′, where Γ′ is an irre...

We sketch a simplification of proofs old results on the arithmeticity group generated by opposing integral unipotent radicals contained in higher rank arithmetic groups.

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 classify the unipotent character sheaves on a fixed connected component of a reductive algebraic group under a mild condition on the characteristic of the ground field.