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One considers Gelfand’s hypergeometric functions on the space of p×q matrices and their generalizations to the case of multi-dimensional matrices of arbitrary order k
p. It is shown that these functions form bases of some
In this paper one considers a unimodular second countable locally compact group G and the homogeneous space X:=H\G, where H is a closed unimodular subgroup of G. Over X complex vector bundles are considered such that H acts on the fibers by a unitary representation ρ with closed image. The...
We review the relationship between pure four-dimensional Seiberg–Witten theory and the periodic Toda chain. We discuss the definition of the prepotential and give two proofs that it satisfies the generalized Witten–Dijkgraaf–Verlinde–Verlinde equations. A number of steps in the definitions and...
The minimal representation π of O(p,q) (p+q: even) is realized on the Hilbert space of square integrable functions on the conical subvariety of Rp+q−2. This model presents a close resemblance of the Schrödinger model of the Segal–Shale–Weil representation of the metaplectic group. We shall give...
We define canonical representations for the hyperboloid of one sheet
and for the Lobachevsky space ℒ=G/K where G=SO0(1,n−1), H=SO0(1,n−2) and K=SO(n−1), as the restriction to G of representations associated with a cone of overgroups
We consider a certain scalar product of symmetric functions which is parameterized by a function r and an integer n. On the one hand we have a fermionic representation of this scalar product. On the other hand we get a representation of this product with the help of multi-integrals. This gives...
We present a combinatorial generalization of the Springer correspondence of the classical groups of Lie type B and C. It is known that the Springer modules yield the tempered irreducible modules with real central character of a graded Hecke algebra of the same Lie type and with equal labels. We...
We discuss zeta extensions in the sense of Kurokawa and Wakayama, Proc. Japan Acad. 2002, for constructing new zeta functions from a given zeta function. This notion appeared when we introduced higher zeta functions such as higher Riemann zeta functions in Kurokawa et al., Kyushu Univ. Preprint,...
We determine the Hilbert series of measures of entanglement for 4 qubits. Various techniques of constructive invariant theory are applied to prove the formula.
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