Related papers: A Basis for the Symplectic Group Branching Algebra

A Chevalley type integral basis for the ortho-symplectic Lie superalgebra is constructed. The simple modules of the ortho-symplectic supergroup over an algebraically closed field of prime characteristic not equal to 2 are classified, where…

In this note we determine the irreducible square integrable representations of a simple group which admits an admissible restriction to a subgroup $H$ locally isomorphic to $SL_2(\mathbb R).$ We show such representation is holomorphic and…

In the representation theory of simple Lie algebras, we consider the problem of constructing a monomial basis in an arbitrary irreducible finite-dimensional highest weight module. We construct a PBW-type basis in every finite-dimensional…

We describe the structure of the Lie groups endowed with a left-invariant symplectic form, called symplectic Lie groups, in terms of semi-direct products of Lie groups, symplectic reduction and principal bundles with affine fiber. This…

text of abstract (We present a utilitarian review of the family of matrix groups $Sp(2n,\Re)$, in a form suited to various applications both in optics and quantum mechanics. We contrast these groups and their geometry with the much more…

Let $G$ be a finite group and $H$ a normal subgroup. Starting from $G$-spin models, in which a non-Abelian field ${\mathcal{F}}_H$ w.r.t. $H$ carries an action of the Hopf $C^*$-algebra $D(H;G)$, a subalgebra of the quantum double $D(G)$,…

We consider the (extended) metaplectic representation of the semidirect product $\mathcal{G}={\mathbb H}^d\rtimes Sp(d,{\mathbb R})$ between the Heisenberg group and the symplectic group. Subgroups $H=\Sigma \rtimes D$, with $\Sigma$ being…

The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…

Using the symplectic geometry of certain manifolds which appear naturally in Lie theory, we define an invariant which assigns a graded abelian group to an oriented link. The relevant manifolds are transverse slices to certain nilpotent…

Let $F$ be a finite field, and let $\mathbb{E}$ be either a quadratic field extension $E/F$ or the split algebra $F \oplus F$. We study distinguished representations of $\rm{SL}_{2n}(F)$ by the subgroup $H_{\flat} := \rm{SL}_{2n}(F) \cap…

The split basis of an irreducible representation of the symmetric group, $S_{n+m}$, is the basis which is adapted to direct product subgroups of the form $S_{n} \times S_{m}$. In this article we have calculated symmetric group subduction…

We define the singular Hecke algebra ${\mathcal H} (SB_n)$ as the quotient of the singular braid monoid algebra ${\mathbb C} (q) [SB_n]$ by the Hecke relations $\sigma_k^2 = (q-1) \sigma_k +q$, $1 \le k\le n-1$, and define the Markov traces…

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 f is a non-trivial irreducible…

For the symplectic Grassmannian $\text{SpG}(2,2n)$ of $2$-dimensional isotropic subspaces in a $2n$-dimensional vector space over an algebraically closed field of characteristic zero endowed with a symplectic form and with the natural…

We relate the classes of unitary and calibrated representations of cyclotomic Hecke algebras and, in particular, we show that for the most important deformation parameters these two classes coincide. We classify these representations in…

We give alternative computations of the Schur multiplier of $Sp(2g,\mathbb Z/D\mathbb Z)$, when $D$ is divisible by 4 and $g\geq 4$: a first one using $K$-theory arguments based on the work of Barge and Lannes and a second one based on the…

The algebra of symmetric tensors $S(X):= H^0(X, \sf{S}^{\bullet} T_X)$ of a projective manifold $X$ leads to a natural dominant affinization morphism $$ \varphi_X: T^*X \longrightarrow \mathcal{Z}_X:= \text{Spec} S(X). $$ It is shown that…

Starting with an O(2)-principal fibration over a closed oriented surface F_g, g>=1, a 2-fold covering of the total space is said to be special when the monodromy sends the fiber SO(2) = S^1 to the nontrivial element of Z_2. Adapting D…

A Gelfand model for a semisimple algebra A over C is a complex linear representation that contains each irreducible representation of A with multiplicity exactly one. We give a method of constructing these models that works uniformly for a…

In this chapter we give a geometric representation of $H_{n}(B;\mathbb{L})$ classes, where $\mathbb{L}$ is the $4$-periodic surgery spectrum, by establishing a relationship between the normal cobordism classes…