Related papers: Branching laws for square integrable representatio…
We consider quantum group representations for a semisimple algebraic group G at a complex root of unity q. Here q is allowed to be of any order. We revisit some fundamental results of Parshall-Wang and Andersen-Polo-Wen from the 90's. In…
We show that finite quasisimple groups of Lie type in characteristic $p$ with an irreducible representation of prime degree $r$ over a finite field of characteristic $p$ have orders bounded above by a function of $r$, independent of $p$. We…
Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of…
The aim of this note is to give a gentle introduction to algebras of partial triangulations of marked surfaces, following the structure of a talk given during the 49th symposium on ring theory and representation theory, held in Osaka. This…
We investigate the joint action of two real forms of a semi-simple complex Lie group S by left and right multiplication. After analyzing the orbit structure, we study the CR structure of closed orbits. The main results are an explicit…
We relate the linear asymptotic representation theory of the symmetric groups to its spin counterpart. In particular, we give explicit formulas which express the normalized irreducible spin characters evaluated on a strict partition $\xi$…
We study the subgroup structure, Hecke algebras, quasi-regular representations, and asymptotic properties of some fractal groups of branch type. We introduce parabolic subgroups, show that they are weakly maximal, and that the corresponding…
We classify the finite-dimensional irreducible linear representations of the Baumslag-Solitar groups BS(p,q) = < a, b | a b^p = b^q a > for relatively prime p and q. The general strategy of the argument is to consider the matrix group given…
Soft theorems for the form factors of 1/2-BPS and Konishi operator supermultiplets are derived at tree level in N=4 SYM theory. They have a form identical to the one in the amplitude case. For MHV sectors of stress tensor and Konishi…
In this paper, we continue with the results in \cite{Pg} and compute the group of quasi-isometries for a subclass of split solvable unimodular Lie groups. Consequently, we show that any finitely generated group quasi-isometric to a member…
It is shown that supersymmetric integrable models in two dimensions, both relativistic (i.e. super-Toda type theories) and non-relativistic (reductions of super-KP hierarchies) can be associated to general Poisson-brackets structures given…
We discuss the possibility of very regular subgroups of a Lie group, in presence of an index figure. Further, representations that reduce action to a very regular boundary.
In this paper we describe the derivations of orthosymplectic Lie superalgebras over a superring. In particular, we derive sufficient conditions under which the derivations can be expressed as a semidirect product of inner and outer…
The exactly integrable systems connected with semisimple series $A$ for arbitrary grading are presented in explicit form. Their general solutions are expressed in terms of the matrix elements of various fundamental representations of $A_n$…
We determine the decomposition of the restriction of a length-one toral supercuspidal representation of a connected reductive group to the algebraic derived subgroup, in terms of parametrizing data, and show this restriction has…
The main result of this article is an application of the theory of invariant convex cones of Lie algebras to the study of unitary representations of Lie supergroups. It also includes an exposition of recent results of the second author on…
We complete the classification of half-supersymmetric branes in toroidally compactified IIA/IIB string theory in terms of representations of the T-duality group. As a by-product we derive a last wrapping rule for the space-filling branes.…
The problem of reduction of multisymplectic manifolds by the action of Lie groups is stated and discussed, as a previous step to give a fully covariant scheme of reduction for classical field theories with symmetries.
Associative conformal algebras of conformal endomorphisms are of essential importance for the study of finite representations of conformal Lie algebras (Lie vertex algebras). We describe all semisimple algebras of conformal endomorphisms…
Let $\mathfrak{o}$ be a compact discrete valuation ring with maximal ideal $\mathfrak{p}$ such that the finite residue field $\mathfrak{o}/\mathfrak{p}$ has characteristic $p.$ For $r\geq2$ and $p=2,$ we obtain the branching rules for the…