## 2007/2008NxZ~i[̂m点i~wj

ꏊF    wȊwȁij1K 126
ԁF    Ηj 16:30 - 18:00
blF 哇Yiakagi.ms.u|tokyo.ac.jpjCяrsioms.u|tokyo.ac.jpj

• 102
ut: Pablo RamacheriGottingenj
\: Invariant integral operators on affine G-varieties and their kernels
We consider certain invariant integral operators on a smooth affine variety M carrying the action of a reductive algebraic group G, and assume that G acts on M with an open orbit. Then M is isomorphic to a homogeneous vector bundle, and can locally be described via the theory of prehomogenous vector spaces. We then study the Schwartz kernels of the considered operators, and give a description of their singularities using the calculus of b-pseudodifferential operators developed by Melrose. In particular, the restrictions of the kernels to the diagonal can be described in terms of local zeta functions.
• 109
ut: Michaël PevzneriUniversité de Reimsj
\: Rankin-Cohen brackets and covariant quantization
The particular geometric structure of causal symmetric spaces permits the definition of a covariant quantization of these homogeneous manifolds. Composition formulae (#-products) of quantizad operators give rise to a new interpretation of Rankin-Cohen brackets and allow to connect them with the branching laws of tensor products of holomorphic discrete series representations.
• 102516:30-18:00i052jC103015:00-16:30i126jC11116:30-18:00i052j, 11615:00-16:30i126j
ut: Michaël PevzneriUniversité de Reimsj
\: Quantization of symmetric spaces and representation
The goal of this series of lectures will be to describe and compare two intimately related but nevertheless fundamentally different methods of quantization of symmetric spaces : on the one hand deformation quantization and symbolic calculus on the other hand. We shall also discuss interesting connections with the representation theory of semi-simple Lie groups.
• 1030
ut: {v`i吔j
\: On Weyl groups for parabolic subalgebras
Let \${\mathfrak g}\$ be a complex semisimple Lie algebra. We call a parabolic subalgebra \${\mathfrak p}\$ of \${\mathfrak g}\$ normal, if any parabolic subalgebra which has a common Levi part with \${\mathfrak p}\$ is conjugate to \${\mathfrak p}\$ under an inner automorphism of \${\mathfrak g}\$. For a normal parabolic subalgebra, we have a good notion of the restricted root system or the little Weyl group. We have a comparison result on the Bruhat order on the Weyl group for \${\mathfrak g}\$ and the little Weyl group. We also apply this result to the existence problem of the homomorphisms between scalar generalized Verma modules.
• 116
ut: Xe ׎iLj
\: Multiplicity-free decompositions of the minimal representation of the indefinite orthogonal group
A unitary representation of a reductive Lie group can decompose when restricted to a subgroup which is a symmetric pair with finite or infinite multiplicity. On the other hand, T. Kobayashi proved that an irreducible unitary highest weight representation of scalar type decomposes with multiplicity-free when restricted to any subgroup which is a semisimple symmetric pair, and R. Howe proved that the Weil representation decomposes with multiplicity-free when restricted to any subgroup which is a dual pair.
In this talk, with respect to the minimal representation of the indefinite orthogonal group which was constructed by Kazhdan, Kostant, Binegar-Zierau and Kobayashi-Ørsted, we will show that the multiplicity-free theorem holds when restricted to more subgroups than symmetric subgroups.
• 1113() - 16()
\_V|WE 2007
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• 1120
ut: R ij
\: Asymptotic cone for semisimple elements and the associated variety of degenerate principal series
Let a be a hyperbolic element in a semisimple Lie algebra over the real number field. Let K be the complexification of a maximal compact subgroup of the corresponding real adjoint group. We study the asymptotic cone of the semisimple orbit through a under the adjoint action by K. The resulting asymptotic cone is the associated variety of a degenerate principal series representation induced from the parabolic associated to a.
• 1211
ut: q (w)
\: Characterization of some smooth vectors for irreducible representations of exponential solvable Lie groups
This is a joint work with Jean Ludwig (University of Metz). Let G be an exponential solvable Lie group, and be an irreducible unitary representation of G. By induction from a character on a connected subgroup H, is realized on a Hilbert space of L2-functions on a homogeneous space G/H. We investigate a subspace SE of C-vectors of consisting of functions with a certain property of rapidly decreasing at infinity. We give a description of SE as the space of C-vectors of an extension of to an exponential solvable group containing G.
• 1218
ut: Is (w)
\: On the existence of homomorphisms between principal series of complex semisimple Lie groups
The principal series representations of a semisimple Lie group play an important role in the representation theory. We study the principal series representation of a complex semisimple Lie group and determine when there exists a nonzero homomorphism between the representations.
• 115
ut: Fulton Gonzalez (Tuffs University)
\: Group contractions, invariant differential operators and the matrix Radon transform
Let Mn,k denote the vector space of real n~k matrices. The matrix motion group is the semidirect product (O(n)~O(k)) \ltimes Mn,k, and is the Cartan motion group associated with the real Grassmannian Gn,n+k. The matrix Radon transform is an integral transform associated with a double fibration involving homogeneous spaces of this group. We provide a set of algebraically independent generators of the subalgebra of its universal enveloping algebra invariant under the Adjoint representation. One of the elements of this set characterizes the range of the matrix Radon transform.
• 117i؁j17:00 - 18:00
ut: M (w)
ꏊ: 123
\: Proper actions of SL(2,R) on irreducible complex symmetric spaces
We determine the irreducible complex symmetric spaces on which SL(2,R) acts properly. We use the T. Kobayashi's criterion for the proper actions. Also we use the symmetry or unsymmetry of the weighted Dynkin diagram of the theory of nilpotent orbits.
• 122
ut: 哇 Y (w)
\: Connecion problems for Fuchsian differential equations free from accessory parameters
The classification of Fuchsian equations without accessory parameters was formulated as Deligne-Simpson problem, which was solved by Katz and they are studied by Haraoka and Yokoyama. If the number of singular points of such equations is three, they have no geometric moduli. We give a unified connection formula for such differential equations as a conjecture and show that it is true for the equations whose local monodromy at a singular point has distinct eigenvalues. Other Fuchsian differential equations with accessory parameters and hypergeometric functions with multi-variables are also discussed.
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