Related papers: Good l-filtrations for q-GL_3(k)

Let G be a connected and reductive algebraic group over an algebraically closed field of characteristic p > 0. An interesting class of representations of G consists of those G-modules having a good filtration -- i.e. a filtration whose…

Let $G$ be a connected reductive group over an algebraically closed field $\Bbbk$. Under mild restrictions on the characteristic of $\Bbbk$, we show that any $G$-module with a good filtration also has a good filtration as a module for the…

We investigate rational $G$-modules $M$ for a linear algebraic group $G$ over an algebraically closed field $k$ of characteristic $p > 0$ using filtrations by sub-coalgebras of the coordinate algebra $k[G]$ of $G$. Even in the special case…

Let G be a connected reductive linear algebraic group over a field k of characteristic p>0. Let p be large enough with respect to the root system. We show that if a finitely generated commutative k-algebra A with G-action has good…

Let $G$ be a semisimple algebraic group over an algebraically closed field $k$ of positive characteristic $p$. Under some restrictions on the size of $p$, the present paper establishes new results on the $G$-module structure of…

Let G be a linear algebraic group over an algebraically closed field of characteristic p whose corresponding root system is irreducible. In this paper we calculate the Weyl filtration dimension of the induced G-modules, \nabla(\lambda) and…

Let $k$ be an algebraically closed field of positive characteristic, $G$ a reductive group over $k$, and $V$ a finite dimensional $G$-module. Let $B$ be a Borel subgroup of $G$, and $U$ its unipotent radical. We prove that if $S=\Sym V$ has…

Let $G$ be a simple simply connected group scheme defined over ${\mathbb F}_{p}$ and $k$ be an algebraically closed field of characteristic $p>0$. Moreover, let $B$ be a Borel subgroup of $G$ and $U$ be the unipotent radical of $B$. In this…

Let G be GL_N or SL_N as reductive linear algebraic group over a field k of positive characteristic p. We prove several results that were previously established only when N < 6 or p > 2^N. Let G act rationally on a finitely generated…

Let $p$ be a prime number, let $K$ be a $p$-field (a local field with finite residue field of characteristic $p$), let $L$ be a finite galoisian tamely ramified extension of $K$, and let $G=\mathrm{Gal}(L|K)$. Suppose that $L$ is split over…

Let ${\bf G}$ be a connected reductive group over $\bar{\mathbb{F}}_q$, the algebraically closure of $\mathbb{F}_q$ (the finite field with $q=p^e$ elements), with the standard Frobenius map $F$. Let ${\bf B}$ be an $F$-stable Borel…

The third homology group of GL_n(R) is studied, where R is a `ring with many units' with center Z(R). The main theorem states that if K_1(Z(R))_Q \simeq K_1(R)_Q, (e.g. R a commutative ring or a central simple algebra), then H_3(GL_2(R), Q)…

Let $G$ be a finite group and $H$ a normal subgroup of prime index $p$. Let $V$ be an irreducible ${\mathbb F}H$-module and $U$ a quotient of the induced ${\mathbb F}G$-module $V\kern-3pt\uparrow$. We describe the structure of $U$, which is…

Let $G$ be a semisimple algebraic group over a field of characteristic $p > 0$. We prove that the dual Weyl modules for $G$ all have $p$-filtrations when $p$ is not too small. Moreover, we give applications of this theorem to…

Let $G$ be a simple, simply connected algebraic group over an algebraically closed field of prime characteristic $p>0$. Recent work of Kildetoft and Nakano and of Sobaje has shown close connections between two long-standing conjectures of…

We investigate the representation theory of domestic group schemes $\mathcal{G}$ over an algebraically closed field of characteristic $p > 2$. We present results about filtrations of induced modules, actions on support varieties, Clifford…

We consider a generalization of Donkin-Koppinen filtrations for coordinate superalgebras of general linear supergroups. More precisely, if $G=GL(m|n)$ is a general linear supergroup of (super)degree $(m|n)$, then its coordinate superalgebra…

We prove that in positive characteristic a module with good filtration for a group of type E6 restricts to a module with good filtration for a subgroup of type F4. (Recall that a filtration of a module for a semisimple algebraic group is…

We first define the notion of good filtration dimension and Weyl filtration dimension in a quasi-hereditary algebra. We calculate these dimensions explicitly for all irreducible modules in SL_2 and SL_3. We use these to show that the global…

This paper is the continuation of \cite{CXY}. Let ${\bf G}$ be a simply connected semisimple algebraic group over $\Bbbk=\bar{\mathbb{F}}_q$, the algebraically closure of $\mathbb{F}_q$ (the finite field with $q=p^e$ elements), and $F$ be…