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Let $\mathrm{SO}^+(p,q)$ denote the identity connected component of the real orthogonal group with signature $(p,q)$. We give a complete description of the spaces of continuous and generalized translation- and $\mathrm{SO}^+(p,q)$-invariant…

We study Demazure modules which occur in a level $\ell$ irreducible integrable representation of an affine Lie algebra. We also assume that they are stable under the action of the standard maximal parabolic subalgebra of the affine Lie…

In this paper we prove that the quantum Stokes matrices of the quantum differential equation at a second order pole give rise to representations of the quantum group $U_q(\frak{gl}_n)$. We explain our results from the viewpoint of…

In this paper, we prove stability results about orthogonal groups over finite commutative rings where 2 is a unit. Inspired by Putman and Sam (2017), we construct a category $\mathbf{OrI}(R)$ and prove a Noetherianity theorem for the…

We start with a small paradigm shift about group representations, namely the observation that restriction to a subgroup can be understood as an extension-of-scalars. We deduce that, given a group $G$, the derived and the stable categories…

For groups of prime order, equivariant stable maps between equivariant representation spheres are investigated using the Borel cohomology Adams spectral sequence. Features of the equivariant stable homotopy category, such as stability and…

Let $G$ be the $F$-points of a connected reductive group over a non-archimedean local field $F$ of residue characteristic $p$ and $R$ be a commutative ring. Let $P=LU$ be a parabolic subgroup of $G$ and $Q$ be a parabolic subgroup of $G$…

In this article we describe extensions of some K-theory classes of Heisenberg modules over higher-dimensional noncommutative tori to projective modules over crossed products of noncommutative tori by finite cyclic groups, aka noncommutative…

We consider compact matrix quantum groups whose fundamental corepresentation matrix has entries which are partial isometries with central support. We show that such quantum groups have a simple representation as semi-direct product quantum…

Several classes of irreducible orthogonal representations of compact Lie groups that are of importance in Differential Geometry have the property that the second osculating spaces of all of their nontrivial orbits coincide with the…

This paper is an exposition of the completion of a modular group with respect to its inclusion into SL_2(Q) and the connection with the theory of modular forms and variations of mixed Hodge structure over modular curves. Among the goals of…

Let $Q$ be an algebraic group and $V$ a $Q$-module. The index of $V$ is the minimal codimension of the $Q$-orbits in the dual space $V^*$. There is a general inequality, due to Vinberg, relating the index of $V$ and the index of…

We study the Chow ring of the moduli stack $\mathfrak{M}_{g,n}$ of prestable curves and define the notion of tautological classes on this stack. We extend formulas for intersection products and functoriality of tautological classes under…

The representations of the Schr\"odinger group in one space dimension are explicitly constructed in the basis of the harmonic oscillator states. These representations are seen to involve matrix orthogonal polynomials in a discrete variable…

Let $G$ be a simple and simply connected algebraic group over an algebraically closed field $\Bbbk$ of characteristic $p>0$. We establish an isomorphism of $G$-modules between a direct sum of modules $\text{St} \otimes \text{St}$ and a…

We study simple and projective modules of a certain class of Ehresmann semigroups, a well-studied generalization of inverse semigroups. Let $S$ be a finite right (left) restriction Ehresmann semigroup whose corresponding Ehresmann category…

We begin to study Steinberg groups associated with a locally isotropic reductive group $G$ over a arbitrary ring. We propose a construction of such a Steinberg group functor as a group object in a certain completion of the category of…

Motivated by the relation between Schur algebra and the group algebra of a symmetric group, along with other similar examples in algebraic Lie theory, Min Fang and Steffen Koenig addressed some behaviour of the endomorphism algebra of a…

We classify quadratic SL(2,K)- and sl(2,K)-modules by crude computation, generalizing in the first case a Theorem proved independently by F.-G. Timmesfeld and S. Smith. The paper is the first of a series dealing with linearization results…

We prove the following criterion for the pro-representability of the deformation cohomology of a commutative formal Lie group. Let f be a flat and separated morphism between noetherian schemes. Assume that the target of f is flat over the…