Showing papers by "Vladimír Souček published in 2016"
TL;DR: In this paper, a relative version of Kostant's harmonic theory and a relative homology group are used to realize representations with lowest weight in one (regular or singular) affine Weyl orbit.
9 citations
TL;DR: In this paper, the Fischer decomposition of spinor-valued homogeneous polynomials is decomposed in terms of irreducible representations of the symplectic group Sp(p).
Abstract: Spaces of spinor-valued homogeneous polynomials, and in particular spaces of spinor-valued spherical harmonics, are decomposed in terms of irreducible representations of the symplectic group Sp(p). These Fischer decompositions involve spaces of homogeneous, so-called osp(4|2)-monogenic polynomials, the Lie super algebra osp(4|2) being the Howe dual partner to the symplectic group Sp(p). In order to obtain Sp(p)-irreducibility, this new concept of osp(4|2)-monogenicity has to be introduced as a refinement of quaternionic monogenicity; it is defined by means of the four quaternionic Dirac operators, a scalar Euler operator E underlying the notion of symplectic harmonicity and a multiplicative Clifford algebra operator P underlying the decomposition of spinor space into symplectic cells. These operators E and P, and their Hermitian conjugates, arise naturally when constructing the Howe dual pair osp(4|2)×Sp(p), the action of which will make the Fischer decomposition multiplicity free. Copyright © 2016 John Wiley & Sons, Ltd.
7 citations
TL;DR: In this paper, the theory of skew duality was used to show that decomposing the tensor product of irreducible representations of the symplectic group $Sp 2m = Sp 2m}(C) is equivalent to branching from $Sp n 2n to Sp 2n n 1/2n/1/2k/n 2n/k/k, where n is the number of positive integers.
Abstract: We use the theory of skew duality to show that decomposing the tensor product of $k$ irreducible representations of the symplectic group $Sp_{2m} = Sp_{2m}(C)$ is equivalent to branching from $Sp_{2n}$ to $Sp_{2n_1}\times\cdots\times Sp_{2n_k}$ where $n, n_1,\ldots, n_k$ are positive integers such that $n = n_1+\cdots+n_k$ and the $n_j$'s depend on $m$ as well as the representations in the tensor product. Using this result and a work of J. Lepowsky, we obtain a skew Pieri rule for $Sp_{2m}$, i.e., a description of the irreducible decomposition of the tensor product of an irreducible representation of the symplectic group $Sp_{2m}$ with a fundamental representation.
5 citations
TL;DR: In this article, a geometric construction of the BGG resolutions in singular infinitesimal character in the case of 1-graded complex Lie algebras of type A is given.
Abstract: We give a geometric construction of the BGG resolutions in singular infinitesimal character in the case of 1-graded complex Lie algebras of type A.
4 citations
TL;DR: In this paper, the authors introduce integral transforms that map slice monogenic functions to monogenic function and show that one of these integral transforms is useful to define a functional calculus depending on a parameter for n-tuples of bounded operators.
Abstract: In this paper, we introduce some integral transforms that map slice monogenic functions to monogenic functions. We then show that one of these integral transforms, which is based on the Cauchy formula of slice monogenic functions, is useful to define a functional calculus depending on a parameter for n-tuples of bounded operators. Copyright © 2015 John Wiley & Sons, Ltd.