Homological vanishing for the Steinberg representation
                    
                        
                            نویسندگان
                            
                            
                        
                        
                    
                    
                    چکیده
منابع مشابه
The Steinberg Representation
Introduction. Group representations occupy a sort of middle ground between abstract groups and transformation groups, i.e., groups acting in concrete ways as permutations of sets, homeomorphisms of topological spaces, diffeomorphisms of manifolds, etc. The requirement that the elements of a group act as linear operators on a vector space limits somewhat the complexity of the action without sacr...
متن کاملHomological Algebra for the Representation Green Functor for Abelian Groups
In this paper we compute some derived functors Ext of the internal homomorphism functor in the category of modules over the representation Green functor. This internal homomorphism functor is the left adjoint of the box product. When the group is a cyclic 2-group, we construct a projective resolution of the module fixed point functor, and that allows a direct computation of the graded Green fun...
متن کاملRepresentation theory and homological stability
We introduce the idea of representation stability (and several variations) for a sequence of representations Vn of groups Gn. A central application of the new viewpoint we introduce here is the importation of representation theory into the study of homological stability. This makes it possible to extend classical theorems of homological stability to a much broader variety of examples. Represent...
متن کاملBessel models and L-functions for the Steinberg representation of GSp4
We obtain explicit formulas for the test vector in the Bessel model and derive the criteria for existence and uniqueness for Bessel models for the unramified, quadratic twists of the Steinberg representation π of GSp4(F ), where F is a non-archimedean local field of characteristic zero. We also give precise criteria for the Iwahori spherical vector in π to be a test vector. We apply the formula...
متن کاملThe behavior of homological dimensions
Let R be a commutative noetherian ring. We study the behavior of injectiveand at dimension of R-modules under the functors HomR(-,-) and -×R-.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2018
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x18007029