K-TYPES OF SU(1, n) REPRESENTATIONS AND RESTRICTION OF COHOMOLOGY
نویسندگان
چکیده
This paper shows that the highest weights of the K-types of any irreducible admissible representation of SU(1, n) are determined by certain restriction maps from u to u ∩ k cohomology. In particular, the image of these maps determines a set of points in a Cartan subalgebra. It is proved that the highest weights of the K-types are given by intersecting a translate of the root lattice with the closed convex hull of the points determined by the restriction maps.
منابع مشابه
ON THE (g,K)-COHOMOLOGY OF CERTAIN THETA LIFTS
It is well-known that one of the most important ways of constructing cohomology for an arithmetic quotient Γ\X, where X is the symmetric space associated with a semi-simple Lie group G with finite center and Γ is a discrete subgroup of G, is through the use of Matsushima’s formula, namely by exhibiting irreducible unitary representations with non-zero continuous cohomology which occur in L2(Γ\G...
متن کاملThe Cohomology of Weight Varieties
We describe the cohomology ring of the symplectic reductions by tori of coadjoint orbits, or weight varieties. Weight varieties arise from representation theory considerations, and are temed as such because they are the symplectic analogue of the T-isotypic components (weight spaces) of irreducible representations of G. Recently, Tolman and Weitsman expressed the (ordinary) cohomology ring for ...
متن کاملRestriction Varieties and Geometric Branching Rules
This paper develops a new method for studying the cohomology of orthogonal flag varieties. Restriction varieties are subvarieties of orthogonal flag varieties defined by rank conditions with respect to (not necessarily isotropic) flags. They interpolate between Schubert varieties in orthogonal flag varieties and the restrictions of general Schubert varieties in ordinary flag varieties. We give ...
متن کاملOn the Cohomology of Weakly Almost Periodic Group Representations
We initiate a study of cohomological aspects of weakly almost periodic group representations on Banach spaces, in particular, isometric representations on reflexive Banach spaces. Using the Ryll-Nardzewski fixed point Theorem, we prove a vanishing result for the restriction map (with respect to a subgroup) in the reduced cohomology of weakly periodic representations. Combined with the Alaoglu-B...
متن کاملLocal rigidity of discrete groups acting on complex hyperbolic space
The superrigidity theorem of Margulis, see Zimmer [17], classifies finite dimensional representations of lattices in semi-simple Lie groups of real rank strictly larger than 1. It is a fundamental problem to obtain the classification of finite dimensional representations of lattices in rank I semi-simple Lie groups. That this problem will be considerably harder than the previous one is suggeste...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999