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作者：Gindikin, S; Krötz, B; Olafsson, G
作者单位：Rutgers University System; Rutgers University New Brunswick; University of Oregon; Louisiana State University System; Louisiana State University
摘要：Let G/H be a semisimple symmetric space. The main tool to embed a principal series representation of G into L-2(G/H) are the H-invariant distribution vectors. If G/H is a non-compactly causal symmetric space, then G/H can be realized as a boundary component of the complex crown Xi. In this article we construct a minimal G-invariant subdomain Xi(H) of Xi with G/H as Shilov boundary. Let pi be a spherical principal series representation of G. We show that the space of H-invariant distribution ve...
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作者：Feichtner, EM; Yuzvinsky, S
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Oregon
摘要：We study a graded algebra D = D(L, g) over Z defined by a finite lattice L and a subset g in L, a so-called building set. This algebra is a generalization of the cohomology algebras of hyperplane arrangement compactifications found in work of De Concini and Procesi [2]. Our main result is a representation of D, for an arbitrary atomic lattice L, as the Chow ring of a smooth toric variety that we construct from L and g. We describe this variety both by its fan and geometrically by a series of b...
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作者：Mavlyutov, AR
作者单位：Indiana University System; Indiana University Bloomington
摘要：One can deform the complex structure of Calabi-Yau hypersurfaces in toric varieties by changing the coefficients of the defining polynomial. However, there must also exist non-polynomial deformations of the Calabi-Yau hypersurfaces which cannot be realized inside the ambient toric variety. In this paper, we have constructed the missing non-polynomial deformations, which are induced by an automorphism on the open part of the ambient toric variety.
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作者：Daskalopoulos, P; Lee, KA
作者单位：Columbia University; Seoul National University (SNU)
摘要：We study the all time regularity of the free-boundary problem associated to the deformation of a compact weakly convex surface Sigma in R-3, with a flat side, by its Gaussian Curvature. We show that under certain necessary regularity and non-degeneracy initial conditions the interface separating the flat from the strictly convex side, remains smooth on 0
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作者：Kerov, S; Olshanski, G; Vershik, A
作者单位：Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences
摘要：The infinite symmetric group S(infinity), whose elements are finite permutations of {1,2,3,...}, is a model example of a big group. By virtue of an old result of Murray-von Neumann, the one-sided regular representation of S(infinity) in the Hilbert space l(2)(S(infinity)) generates a type II1 von Neumann factor while the two-sided regular representation is irreducible. This shows that the conventional scheme of harmonic analysis is not applicable to S(infinity): for the former representation, ...
