Extending Representations of Subgroups and the Duality of Induction and Restriction

نویسنده

  • IAIN RAEBURN
چکیده

Suppose that G is a locally compact group and U is a representation of a closed subgroup H of G on a Hilbert space H. We use nonabelian duality for crossed products of C∗-algebras to study the following problem: when does U extend to a representation of G on the same space H?

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Duality of Restriction and Induction for C-coactions

Consider a coaction δ of a locally compact group G on a C-algebra A, and a closed normal subgroup N of G. We prove, following results of Echterhoff for abelian G, that Mansfield’s imprimitivity between A ×δ| G/N and A ×δ G ×δ̂,r N implements equivalences between Mansfield induction of representations from A×G/N to A×G and restriction of representations fromA×G×rN to A × G, and between restrictio...

متن کامل

Extension Problems For

When A = C, H = N is normal and K = G, this is a classical problem which has been studied using a variety of methods (see [3, 8, 1, 12], for example), and its solution for irreducible representations is a crucial ingredient in the Mackey machine [17]. In [10], we considered the problem for C-dynamical systems with H = N normal and K = G, and found a condition on the induced representation IndGN...

متن کامل

THE BURGER-SARNAK METHOD AND OPERATIONS ON THE UNITARY DUAL OF GL(n)

We study the effect of restriction to Levi subgroups, induction from Levi subgroups, and tensor product, on unitary representations of GL(n) over a local field k. These results give partial answers to questions raised by

متن کامل

Distinguished positive regular representations

Let $G$ be a tamely ramified reductive $p$-adic‎ ‎group‎. ‎We study distinction of a class of irreducible admissible representations‎ ‎of $G$ by the group of fixed points $H$ of an involution‎ ‎of $G$‎. ‎The representations correspond to $G$-conjugacy classes of‎ ‎pairs $(T,phi)$‎, ‎where $T$ is a‎ ‎tamely ramified maximal torus of $G$ and $phi$ is a quasicharacter‎ ‎of $T$ whose restriction t...

متن کامل

Cohomology of Standard Modules on Partial Flag Varieties

Cohomological induction gives an algebraic method for constructing representations of a real reductive Lie group G from irreducible representations of reductive subgroups. Beilinson-Bernstein localization alternatively gives a geometric method for constructing Harish-Chandra modules for G from certain representations of a Cartan subgroup. The duality theorem of Hecht, Miličić, Schmid and Wolf e...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008