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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...
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
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
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...
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 determine the Hilbert series of measures of entanglement for 4 qubits. Various techniques of constructive invariant theory are applied to prove the formula.
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 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...
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,...
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