Related papers: Reproducing subgroups of $Sp(2,\mathbb{R})$. Part …

A new set of elementary symplectic elements is described, It is shown that these also generate the elementary symplectic group {\rm ESp}$_{2n}(R)$. These generators are more symmetrical than the usual ones, and are useful to study the…

In this paper, we obtain a full classification of reductive dual pairs in a, real or complex, Lie superalgebra $\mathfrak{spo}(E)$ and Lie supergroup $\textbf{SpO}(E)$. Moreover, by looking at the natural action of the orthosymplectic Lie…

Following the theory of principal $\infty$-bundles of Niklaus-Schreiber-Steveson, we develop a homotopy categorification of Hopf algebras, which model quantum groups. We study their higher-representation theory in the setting of…

In this note, we introduce a relative (or Lagrangian) version of the Seidel homomorphism that assigns to each homotopy class of paths in Ham(M), starting at the identity and ending on the subgroup that preserves a given Lagrangian…

We categorify a quantized Heisenberg algebra associated to a finite subgroup of SL(2,C).

We classify non-polar irreducible representations of connected compact Lie groups whose orbit space is isometric to that of a representation of a finite extension of $Sp(1)^k$ for some $k>0$. It follows that they are obtained from isotropy…

All results concern characteristic 2. Two procedures that to every simple Lie algebra assign simple Lie superalgebras, most of the latter new, are offered. We prove that every simple finite-dimensional Lie superalgebra is obtained as the…

The 2-rank of a compact Lie group $G$ is the maximal possible rank of the elementary 2-subgroup ${\mathbb Z}_{2}\times... {\mathbb Z}_{2}$ of $G$. The study of 2-ranks (and $p$-rank for any prime $p$) of compact Lie groups was initiated in…

In this paper we will study both the finite and infinite-dimensional representations of the symplectic Lie algebra $\mathfrak{sp}(2n)$ and develop a polynomial model for these representations. This means that we will associate a certain…

This work is motivated by an investigation into whether, and if so how, certain well known facts about Lie groups manifest in the context of group schemes over rings of integers of local fields. There are the following well-known relations…

Let $(S,*)$ be an involutive local ring and let $U(2m,S)$ be the unitary group associated to a nondegenerate skew hermitian form defined on a free $S$-module of rank $2m$. A presentation of $U(2m,S)$ is given in terms of Bruhat generators…

We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically…

We give various realizations of the adjoint orbits of a semi-simple Lie group and describe their symplectic geometry. We then use these realizations to identify a family of Lagrangean submanifolds of the orbits.

To the integral symplectic group Sp(2g,Z) we associate two posets of which we prove that they have the Cohen-Macaulay property. As an application we show that the locus of marked decomposable principally polarized abelian varieties in the…

We introduce a remarkable subset "the stem" of the set of positive roots of a reduced root system. The stem determines several interesting decompositions of the corresponding reductive Lie algebra. It gives also a nice simple three…

Let $\ell$ be a prime divisor of the order of a finite unitary reflection group. We classify up to conjugacy the parabolic and reflection subgroups that are minimal with respect to inclusion, subject to containing an $\ell$-Sylow subgroup.…

Following our approach to metric Lie algebras developed in math.DG/0312243 we propose a way of understanding pseudo-Riemannian symmetric spaces which are not semi-simple. We introduce cohomology sets (called quadratic cohomology) associated…

For a given abelian group G, we classify the isomorphism classes of G-gradings on the simple restricted Lie algebras of types W(m;1) and S(m;1) (m>=2), in terms of numerical and group-theoretical invariants. Our main tool is automorphism…

Let $\g$ be a complex orthogonal or symplectic Lie algebra and $\g'\subset \g$ the Lie subalgebra of rank $\rk \g'=\rk \g-1$ of the same type. We give an explicit construction of generators of the Mickelsson algebra $Z_q(\g,\g')$ in terms…

In this paper, we determine the blocks of $\mathcal{O}^\mathfrak{p}$ associated with semisimple Lie algebras of type $E$.