Abstract. We obtain explicit formulas for the product of a deformed Weyl denominator with the character of an irreducible representation of the spin group Spin2r+1(C), which is an analogue of the formulas of Tokuyama for Schur polynomials and Hamel-King for characters of symplectic groups. To give these, we start with a symplectic group and obtain such characters using the Casselman-Shalika for...

We study the general geometrical structure of the coadjoint orbits of a semidirect product formed by a Lie group and a representation of this group on a vector space. The use of symplectic induction methods gives new insight into the structure of these orbits. In fact, each coadjoint orbit of such a group is obtained by symplectic induction on some coadjoint orbit of a " smaller " Lie group. We...

In these notes we construct a quantization functor, associating a Hilbert space H(V ) to a finite dimensional symplectic vector space V over a finite field Fq. As a result, we obtain a canonical model for the Weil representation of the symplectic group Sp (V ). The main technical result is a proof of a stronger form of the Stonevon Neumann theorem for the Heisenberg group over Fq. Our result an...

In these notes we construct a quantization functor, associating an Hilbert space H(V ) to a finite dimensional symplectic vector space V over a finite field Fq. As a result, we obtain a canonical model for the Weil representation of the symplectic group Sp (V ). The main technical result is a proof of a stronger form of the Stone-von Neumann theorem for the Heisenberg group over Fq. Our result ...

Let M be a smooth, closed oriented 4−manifold. An orientation-compatible symplectic structure on M is a closed two form ω such that ω ∧ ω is nowhere vanishing and gives the orientation. Two such symplectic structures ω 1 and ω 2 on M are said to be deformation equivalent if there is an orientation-preserving diffeomorphism φ such that φ * ω 1 and ω 2 are connected by a path of symplectic forms....

Let M be a smooth, closed oriented 4−manifold. An orientation-compatible symplectic structure on M is a closed two form ω such that ω ∧ ω is nowhere vanishing and gives the orientation. Two such symplectic structures ω 1 and ω 2 on M are said to be deformation equivalent if there is an orientation-preserving diffeomorphism φ such that φ * ω 1 and ω 2 are connected by a path of symplectic forms....

A symplectic involution on a K3 surface is an involution which preserves the holomorphic 2-form. We prove that such a symplectic involution acts as the identity on the CH0 group of the K3 surface, as predicted by Bloch’s conjecture. 2010 Mathematics Subject Classification: 14C25, 14J28

The investigation of symmetries b-symplectic manifolds and folded-symplectic is well-understood when the group under consideration a torus (see, for instance, [GMPS,GLPR, GMW18a] [CGP, CM] folded symplectic manifolds). However, reduction theory has not been set in this realm full generality. This fundamental, among other reasons, to advance "quantization commutes with reduction" programme these...