Related papers: Affine Grassmannians for Triality Groups

We give a unified description of twisted forms of classical reductive groups schemes. Such group schemes are constructed from algebraic objects of finite rank, excluding some exceptions of small rank. These objects, augmented odd form…

We prove a criterion for the normality of Schubert varieties in twisted affine Grassmannians in terms of the order of the algebraic fundamental group of a certain Levi subgroup, in particular in small positive characteristic. As an…

A connected component of an affine algebraic group is called periodic if all its elements have finite order. We give a characterization of periodic components in terms of automorphisms with finite number of fixed points. It is also…

Here we demonstrate the emergence of Grassmann variables in matrix models based on the exceptional Jordan algebra. The Grassmann algebras are built naturally using the octonion algebra. We argue the appearance of Grassmann variables…

We investigate the existence of 4-torsion in the integral cohomology of oriented Grassmannians. We prove a general criterion for the appearance of 4-torsion classes based on (twisted) Steenrod squares and show that there are many cases…

In this manuscript, we introduce a new class of linear codes, called affine symplectic Grassmann codes, and determine their parameters, automorphism group, minimum distance codewords, dual code and other key features. These linear codes are…

We have recently proposed a Lagrangian in trace dynamics at the Planck scale, for unification of gravitation, Yang-Mills fields, and fermions. Dynamical variables are described by odd-grade (fermionic) and even-grade (bosonic) Grassmann…

Trinomial varieties are affine varieties given by some special system of equations consisting of polynomials with three terms. Such varieties are total coordinate spaces of normal rational varieties with torus action of complexity one. For…

We observe that, for each positive integer n > 2, each of the Artin groups of finite type A_n, B_n=C_n, and affine type \tilde A_{n-1} and \tilde C_{n-1} is a central extension of a finite index subgroup of the mapping class group of the…

The topology of the smooth moduli space of stable rank 2 bundles over a Riemann surface of genus 3 is related to that of the real Grassmannian Gr_4(R^8).

Brane systems provide a large class of gauge theories that arise in string theory. This paper demonstrates how such brane systems fit with a somewhat exotic geometric object, called the affine Grassmannian. This gives a strong motivation to…

In this paper we consider some classical varieties of linear algebras over the field which has characteristic 0. For every considered variety we take a category of the finite generated free algebras of this variety. And for every this…

We determine the automorphism group for a large class of affine quadric hypersurfaces over a field, viewed as affine algebraic varieties. In particular, we find that the group of real polynomial automorphisms of the n-sphere is just the…

Building on earlier results for regular maps and for orientably regular chiral maps, we classify the non-abelian finite simple groups arising as automorphism groups of maps in each of the 14 Graver-Watkins classes of edge-transitive maps.

The Grassmannian is an important object in Algebraic Geometry. One of the many techniques used to study the Grassmannian is to build a vector space from its points in the projective embedding and study the properties of the resulting linear…

We describe the groups of automorphisms of two generated free braided associative algebras with involutive diagonal braidings over a field of characteristic $\neq 2$. Depending on the form of the diagonal involutive braiding, five different…

The goal of this paper is to provide a method, based on the theory of extensions of left-symmetric algebras, for classifying left-invariant affine structures on a given solvable Lie group of low dimension. To better illustrate our method,…

A functor of sets $\mathbb X$ over the category of $K$-commutative algebras is said to be an affine functor if its functor of functions, $\mathbb A_{\mathbb X}$, is reflexive and $\mathbb X=\Spec \mathbb A_{\mathbb X}$. We prove that affine…

We develop a new method for analyzing moduli problems related to the stack of pure coherent sheaves on a polarized family of projective schemes. It is an infinite-dimensional analogue of geometric invariant theory. We apply this to two…

We formulate and prove a profinite rigidity theorem for the twisted Alexander polynomials up to several types of finite ambiguity. We also establish torsion growth formulas of the twisted homology groups in a $\mathbb{Z}$-cover of a…