منابع مشابه
A Branching Law for the Symplectic Groups
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 ...
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In this paper branching rules for the fundamental representations of the symplectic groups in positive characteristic are found. The submodule structure of the restrictions of the fundamental modules for the group Sp2n(K) to the naturally embedded subgroup Sp2n−2(K) is determined. As a corollary, inductive systems of fundamental representations for Sp∞(K) are classified. The submodule structure...
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We study the automorphic theta representation $Theta_{2n}^{(r)}$ on the $r$-fold cover of the symplectic group $Sp_{2n}$. This representation is obtained from the residues of Eisenstein series on this group. If $r$ is odd, $nle r
متن کاملBranching Law for Axons
What determines the caliber of axonal branches? We pursue the hypothesis that the axonal caliber has evolved to minimize signal propagation delays, while keeping arbor volume to a minimum. We show that for a general cost function the optimal diameters of mother 0 d and daughter 1 2 , d d branches at a bifurcation obey a branching law: 2 2 2 0 1 2 d d d Q Q Q . The derivation relies on the fact ...
متن کاملA Basis for the Symplectic Group Branching Algebra
The symplectic group branching algebra, B, is a graded algebra whose components encode the multiplicities of irreducible representations of Sp2n−2(C) in each finite-dimensional irreducible representation of Sp2n(C). By describing on B an ASL structure, we construct an explicit standard monomial basis of B consisting of Sp2n−2(C) highest weight vectors. Moreover, B is known to carry a canonical ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1966
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1966.16.341