This paper gives an explicit argument to show strong boundedness for Sp2n(R) R a ring of S-algebraic integers or semi-local thereby giving quantitative version the abstract result in [15]. The results presented further generalize older regarding by Kedra, Libman and Martin [6] Morris [9] from SLn Sp2n. also completely solve question asymptotic case with that immediately generalizes all other sp...

In this paper we give explicit descriptions of complete sets of mutually unbiased bases (MUBs) and orthogonal decompositions of special Lie algebras sln(C) obtained from commutative and symplectic semifields, and from some other non-semifield symplectic spreads. Relations between various constructions are studied as well. We showed that automorphism groups of complete sets of MUBs and correspon...

Consider a holomorphic torus action on a possibly non-compact Kähler manifold. We show that the higher cohomology groups appearing in the geometric quantization of the symplectic quotient are isomorphic to the invariant parts of the corresponding cohomology groups of the original manifold. For non-Abelian group actions on compact Kähler manifolds, this result was proved recently by Teleman and ...

We prove a companion forms theorem for ordinary n-dimensional automorphic Galois representations, by use of automorphy lifting theorems developed by the second author, and a technique for deducing companion forms theorems due to the first author. We deduce results about the possible Serre weights of mod l Galois representations corresponding to automorphic representations on unitary groups. We ...

Branching laws for the irreducible tensor representations of the general linear and orthogonal groups are well-known. Furthermore, these laws have a simple form [1]. In the case of the symplectic groups, however, the branching law becomes more complicated and is expressed in terms of a determinant. We derive this result here bybrute force applied to the Weyl character formulas, though it could ...

The finite symplectic group Sp(2g) over the field of two elements has a natural representation on the vector space of Siegel modular forms of given weight for the principal congruence subgroup of level two. In this paper we decompose this representation, for various (small) values of the genus and the level, into irreducible representations. As a consequence we obtain uniqueness results for cer...

The Lie-Poisson analogues of the cotangent bundle and coadjoint orbits of a Lie group are considered. For the natural Poisson brackets the symplectic leaves in these manifolds are classified and the corresponding symplectic forms are described. Thus the construction of the Kirillov symplectic form is generalized for Lie-Poisson groups. On leave of absence from LOMI, Fontanka 27, St.Petersburg, ...

Let G be a complex symplectic group. In [K1], we singled out the nilpotent cone N of some reducible G-module, which we call the (1-) exotic nilpotent cone. In this paper, we study the set of G-orbits of the variety N. It turns out that the variety N gives a variant of the Springer correspondence for Weyl groups of type C, but shares a similar flavor with that of type A case. (I.e. there appears...

For certain powers q of odd primes p, and certain integers n ≥ 1, we exhibit explicit rigid local systems on the affine line in characteristic p > 0 whose geometric and arithmetic monodromy groups are Sp(2n, q).

It is shown that the SU(1, 1)-like and SU(2)-like two-photon coherent states can be combined to form a O(3, 2)-like two-photon states. Since the O(3, 2) group has many subgroups, there are also many new interesting new coherent and squeezed two-photon states. Among them is the two-photon sheared state whose symmetry property is like that for the two-dimensional Euclidean group. There are now tw...