In this article we describe the G×G-equivariant K-ring of X, where X is a regular compactification of a connected complex reductive algebraic group G. Furthermore, in the case when G is a semisimple group of adjoint type, and X its wonderful compactification, we describe its ordinary K-ring K(X). More precisely, we prove that K(X) is a free module over K(G/B) of rank the cardinality of the Weyl...

Let g be a semisimple complex Lie algebra and k ⊂ g be any algebraic subalgebra reductive in g. For any simple finite dimensional k-module V , we construct simple (g, k)-modules M with finite dimensional k-isotypic components such that V is a k-submodule of M and the Vogan norm of any simple k-submodule V ′ ⊂ M, V ′ 6≃ V , is greater than the Vogan norm of V . The (g, k)-modules M are subquotie...

The third part of J.-P. Serre’s book Linear Representations of Finite Groups discusses of modular representations, i.e., representations of finite groups over a field of nonzero characteristic. The aim of this work is to complement Serre’s work by introducing the reader to some noncommutative algebra used in the study of modular representations, and in particular to the theory of semisimple and...

Let C be a finite braided multitensor category. Then the end B=∫X∈CX⊗X⁎ is natural Hopf algebra in C. We show that Drinfeld center of isomorphic to category left B-comodules C, and decomposition B into direct sum indecomposable C-subcoalgebras leads B-ComodC C-module subcategories. As an application, we present explicit characterization structure irreducible Yetter-Drinfeld modules over semisim...

We consider bases for the cohomology space of regular semisimple Hessenberg varieties, consisting classes that naturally arise from Białynicki-Birula decomposition varieties. give an explicit combinatorial description support each class, which enables us to compute symmetric group actions on in our bases. then successfully apply results permutohedral varieties explicitly write down class and co...

Kleshchev has recently [7] classi®ed those modules for the symmetric group which have semisimple restriction to any Young subgroup. We determine Ext K Sd …D ;D m† where D l and D m are K Sd -modules of this type, called completely splittable. As a corollary of this and recent work of Kleshchev and Nakano, we can determine ExtGL n…K†……L…l†;L…m†† for certain simple GLn…K†-modules L…l† and L…m†. 1...

In this paper, we propose a scene co-parsing framework to assign pixel-wise semantic labels in weakly-labeled videos, i.e., only videolevel category labels are given. To exploit rich semantic information, we first collect all videos that share the same video-level labels and segment them into supervoxels. We then select representative supervoxels for each category via a supervoxel ranking proce...

Conceptual knowledge is acquired through recurrent experiences, by extracting statistical regularities at different levels of granularity. At a fine level, patterns of feature co-occurrence are categorized into objects. At a coarser level, patterns of concept co-occurrence are categorized into contexts. We present and test CONCAT, a connectionist model that simultaneously learns to categorize o...