Let K be an algebraically closed field of characteristic zero, and let G be a connected reductive algebraic group over K. We address the problem of classifying triples (G, H, V ), where H is a proper connected subgroup of G, and V is a finitedimensional ir ...
Entanglement forging based variational algorithms leverage the bipartition of quantum systems for addressing ground-state problems. The primary limitation of these approaches lies in the exponential summation required over the numerous potential basis stat ...
Let X be a complex projective K3 surface and let T-X be its transcendental lattice; the characteristic polynomials of isometries of T-X induced by automorphisms of X are powers of cyclotomic polynomials. Which powers of cyclotomic polynomials occur? The ai ...
Ulam asked whether all Lie groups can be represented faithfully on a countable set. We establish a reduction of Ulam's problem to the case of simple Lie groups. In particular, we solve the problem for all solvable Lie groups and more generally Lie groups w ...
The arise of disagreement is an emergent phenomenon that can be observed within a growing social group and, beyond a certain threshold, can lead to group fragmentation. To better understand how disagreement emerges, we introduce an analytically tractable m ...
We investigate generalizations along the lines of the Mordell-Lang conjecture of the author's p-adic formal Manin-Mumford results for n-dimensional p-divisible formal groups F. In particular, given a finitely generated subgroup (sic) of F(Q(p)) and a close ...
Let h be a connective homology theory. We construct a functorial relative plus construction as a Bousfield localization functor in the category of maps of spaces. It allows us to associate to a pair (X,H), consisting of a connected space X and an hperfect ...
Let G be a finite subgroup of SU(4) such that its elements have age at most one. In the first part of this paper, we define K-theoretic stable pair invariants on a crepant resolution of the affine quotient C4/G, and conjecture a closed formula for their ge ...
The set of finite binary matrices of a given size is known to carry a finite type AA bicrystal structure. We first review this classical construction, explain how it yields a short proof of the equality between Kostka polynomials and one-dimensional sums t ...
We determine the dimensions of Ext -groups between simple modules and dual generalized Verma modules in singular blocks of parabolic versions of category O for complex semisimple Lie algebras and affine Kac-Moody algebras. ...
Let k be an algebraically closed field of arbitrary characteristic, let G be a simple simply connected linear algebraic group and let V be a rational irreducible tensor-indecomposable finite-dimensional kG-module. For an element g of G we denote by $V_{g}( ...
Let G be either a simple linear algebraic group over an algebraically closed field of characteristic l>0 or a quantum group at an l-th root of unity. The category Rep(G) of finite-dimensional G-modules is non-semisimple. In this thesis, we develop new tech ...
Let G be a simple algebraic group over an algebraically closed field F of characteristic p >= h, the Coxeter number of G. We observe an easy 'recursion formula' for computing the Jantzen sum formula of a Weyl module with p-regular highest weight. We also d ...
We continue our work, started in [9], on the program of classifying triples (X, Y, V), where X, Yare simple algebraic groups over an algebraically closed field of characteristic zero with X < Y, and Vis an irreducible module for Y such that the restriction ...
Ulam asked whether every connected Lie group can be represented on a countable structure. This is known in the linear case. We establish it for the first family of non-linear groups, namely in the nilpotent case. Further context is discussed to illustrate ...
We generalize the fixed-point property for discrete groups acting on convex cones given by Monod in [23] to topological groups. At first, we focus on describing this fixed-point property from a functional point of view, and then we look at the class of gro ...
In a group, the collective dynamics is governed by the inter- actions between individuals, which can manifest differently depending on the available means of communication. In this paper, we compare 3 conditions of communication affordances (global chat, l ...
In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of b-symplectic manifolds started in Guillemin, Miranda, and Pires Adv. Math. 264 (2014), 864-896, we prove a slice theorem for Lie group a ...
We study the spectra of non-regular semisimple elements in irreducible representations of simple algebraic groups. More precisely, we prove that if G is a simply connected simple linear algebraic group and φ : G → GL(V ) is a non-trivial irreducible repres ...
Let G be a simply connected simple algebraic group over an al- gebraically closed field k of characteristic p > 0. The category of rationalG-modules is not semisimple. We consider the question of when the tensorproduct of two simple G-modules L(λ) and L(μ) ...
