Intertwining Operators between Line Bundles on Grassmannians
نویسندگان
چکیده
Let G = GL(n, F ) where F is a local field of arbitrary characteristic, and let π1, π2 be representations induced from characters of two maximal parabolic subgroups P1, P2. We explicitly determine the space HomG (π1, π2) of intertwining operators and prove that it has dimension ≤ 1 in all cases.
منابع مشابه
Reduction and Intertwiners
Reduction of the left regular representation of quantum algebra slq(3) is studied and q-difference intertwining operators are constructed. The irreducible representations correspond to the spaces of local sections of certain line bundles over the q-flag manifold.
متن کاملOn the analytic properties of intertwining operators I: global normalizing factors
We provide a uniform estimate for the $L^1$-norm (over any interval of bounded length) of the logarithmic derivatives of global normalizing factors associated to intertwining operators for the following reductive groups over number fields: inner forms of $operatorname{GL}(n)$; quasi-split classical groups and their similitude groups; the exceptional group $G_2$. This estimate is a key in...
متن کاملAbelian Varieties , Theta Functions and the Fourier Transform
This book is a modern introduction to the theory of abelian varieties and theta functions.Here the Fourier transform techniques play a central role, appearing in several different contexts. In transcendental theory, the usual Fourier transform plays a major role in the representation theory of the Heisenberg group, the main building block for the theory of theta functions. Also, the Fourier tra...
متن کاملFinite rank vector bundles on inductive limits of grassmannians
If P is the projective ind-space, i.e. P is the inductive limit of linear embeddings of complex projective spaces, the Barth-Van de Ven-Tyurin (BVT) Theorem claims that every finite rank vector bundle on P is isomorphic to a direct sum of line bundles. We extend this theorem to general sequences of morphisms between projective spaces by proving that, if there are infinitely many morphisms of de...
متن کاملDERIVED EQUIVALENCES FOR COTANGENT BUNDLES OF GRASSMANNIANS VIA CATEGORICAL sl2 ACTIONS
We construct an equivalence of categories from a strong categorical sl(2) action, following the work of Chuang-Rouquier. As an application, we give an explicit, natural equivalence between the derived categories of coherent sheaves on cotangent bundles to complementary Grassmannians.
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 2013