Rank and duality in representation theory
نویسندگان
چکیده
منابع مشابه
Representation Theory in Complex Rank
The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. The subject of representation theory in complex rank goes back to the papers [DM, De1]. Namely, these papers introduce Karoubian tensor categories Rep(GL t) ([DM, De1]), Rep(O t), Rep(Sp 2t), t ∈ C ([De1]), which are interpolations of the tensor categories of algebraic represen...
متن کاملRank-metric codes and their duality theory
We compare the two duality theories of rank-metric codes proposed by Delsarte and Gabidulin, proving that the former generalizes the latter. We also give an elementary proof of MacWilliams identities for the general case of Delsarte rank-metric codes, in a form that never appeared in the literature. The identities which we derive are very easy to handle, and allow us to re-establish in a very c...
متن کاملKoszul Duality Patterns in Representation Theory
The aim of this paper is to work out a concrete example as wellas to provide the general pattern of applications of Koszul duality to repre-sentation theory. The paper consists of three parts relatively independent ofeach other.The first part gives a reasonably selfcontained introduction to Koszul ringsand Koszul duality. Koszul rings are certain Z-graded rings with particul...
متن کاملRepresentation theory, geometric Langlands duality and categorification
The representation theory of reductive groups, such as the group GLn of invertible complex matrices, is an important topic, with applications to number theory, algebraic geometry, mathematical physics, and quantum topology. One way to study this representation theory is through the geometric Satake correspondence (also known as geometric Langlands duality). This correspondence relates the geome...
متن کاملDuality in Representation
The Schur-Weyl Duality Theorem motivates the general deenition of dual representations. Such representations arise in a very large class of groups, including all compact, nilpotent and semidirect product groups, as well as the complementary groups in the physics literature and the reductive dual pairs in the mathematics literature. Several applications of the notion of duality are given, includ...
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: Japanese Journal of Mathematics
سال: 2020
ISSN: 0289-2316,1861-3624
DOI: 10.1007/s11537-020-1728-3