Related papers: AGC, t-designs and partition sets

We prove the existence of subspace designs with any given parameters, provided that the dimension of the underlying space is sufficiently large in terms of the other parameters of the design and satisfies the obvious necessary divisibility…

We improve on the lower bound of the maximum number of planes in $\operatorname{PG}(8,q)\cong\F_q^{9}$ pairwise intersecting in at most a point. In terms of constant dimension codes this leads to $A_q(9,4;3)\ge q^{12}+…

In this paper we define a generalization of the pentagram map to a map on twisted polygons in the Grassmannian space Gr(n;mn). We define invariants of Grassmannian twisted polygons under the natural action of SL(nm), invariants that define…

Let $H$ be an infinite-dimensional complex Hilbert space and let ${\mathcal L}(H)$ be the logic formed by all closed subspaces of $H$. For every natural $k$ we denote by ${\mathcal G}_{k}(H)$ the Grassmannian consisting of $k$-dimensional…

Let $\phi$ be a collineation of order 3 acting on $PG(2,q^3)$ whose fixed points are exactly an $\mathbb F_q$-plane $\pi_q$. Let $T$ be a point whose orbit under $\phi$ is a triangle and let $S_G$ be the subgroup of $PGL(3,q^3)$ that fixes…

This paper investigates the Terwilliger algebra of some group association schemes related to codes. In addition, it also shows the generators of invariant rings appearing by E-polynomials.

We consider generalized gradients in the general context of $G$-structures. They are natural first order differential operators acting on sections of vector bundles associated to irreducible $G$-representations. We study their geometric…

We study various kinds of Grassmannians or Lagrangian Grassmannians over $\mathbb{R}$, $\mathbb{C}$ or $\mathbb{H}$, all of which can be expressed as $\mathbb{G}/\mathbb{P}$ where $\mathbb{G}$ is a classical group and $\mathbb{P}$ is a…

This paper defines, for each graph $G$, a flag vector $fG$. The flag vectors of the graphs on $n$ vertices span a space whose dimension is $p(n)$, the number of partitions on $n$. The analogy with convex polytopes indicates that the linear…

We show that (equivariant) K-theoretic 3-point Gromov-Witten invariants of genus zero on a Grassmann variety are equal to triple intersections computed in the ordinary (equivariant) K-theory of a two-step flag manifold, thus generalizing an…

Let G be a connected reductive group over an algebraic closure of a finite field Fq. In this paper it is proved that the infinite dimensional Steinberg module of kG defined by N. Xi in 2014 is irreducible when k is a field of positive…

Given a simply-connected simple algebraic group $G$, we determine the tangent space of any Finkelberg-Mirkovi\'c Schubert scheme at the base point of the affine Grassmannian of $G$. As a consequence, we exhibit non-reduced…

Codes in the Grassmannian space have found recently application in network coding. Representation of $k$-dimensional subspaces of $\F_q^n$ has generally an essential role in solving coding problems in the Grassmannian, and in particular in…

In theories like SM or MSSM with a complex gauge group structure the complete set of Feynman diagrams contributed to a particular physics process can be splited to exact gauge invariant subsets. Arguments and examples given in the review…

A geometrical interpretation of Grassmannian anticommuting coordinates is given. They are taken to represent an indefiniteness inherent in every spacetime point on the level of the spacetime foam. This indeterminacy is connected with the…

In: S.G. Barwick and W.A. Jackson. Sublines and subplanes of PG(2,q^3) in the Bruck--Bose representation in PG(6,q). Finite Fields Th. App. 18 (2012) 93--107., the authors determine the representation of order-q-subplanes and…

We present a one-parameter family of constant solutions of the reflection equation and define a family of quantum complex Grassmannians endowed with a transitive action of the quantum unitary group. By computing the radial part of a…

This paper is mainly devoted to constructions of \(q\)-analogs of group divisible designs and their applications. We give a complete description of the action of \(G=\GL(m,q^l)\) on \(\Omega_k^{k-1}\), where $3\leq k\leq \min\left\lbrace…

The study of good nonregular fractional factorial designs has received significant attention over the last two decades. Recent research indicates that designs constructed from quaternary codes (QC) are very promising in this regard. The…

The group $PGL(2,q)$ acts $3$-transitively on the projective line $GF(q) \cup \{\infty\}$. Thus, an orbit of its action on the $k$-subsets of the projective line is the block set of a $3$-$(q+1,k,\lambda)$ design. We find the parameters of…