Download Free Modules Over Rank 2 Klr Algebras Book in PDF and EPUB Free Download. You can read online Modules Over Rank 2 Klr Algebras and write the review.

We study convex order and a cuspidal system for the Khovanov-Lauda-Rouquier (KLR) algebras of twisted affine type. This allows us to classify the irreducible modules over KLR algebras of twisted affine type. Particularly, we are interested in the imaginary modules. They can be constructed from the colored minuscule imaginary modules. We describe explicitly minuscule imaginary modules of certain colors for the Cartan matrices . Moreover, we discuss the the relation between the dimension of minuscule imaginary modules of color and Catalan numbers. For untwisted affine types, Kleshchev and Muth showed that the square of a certain permutation on the imaginary tensor space of a fixed color is a nonzero map. However, it is not the case for twisted affine types. We present a new result that these maps of the imaginary tensor spaces of certain color for some twisted affine types are equal to zero.
This volume is an outgrowth of the program Modular Representation Theory of Finite and p-Adic Groups held at the Institute for Mathematical Sciences at National University of Singapore during the period of 1-26 April 2013. It contains research works in the areas of modular representation theory of p-adic groups and finite groups and their related algebras. The aim of this volume is to provide a bridge — where interactions are rare between researchers from these two areas — by highlighting the latest developments, suggesting potential new research problems, and promoting new collaborations.It is perhaps one of the few volumes, if not only, which treats such a juxtaposition of diverse topics, emphasizing their common core at the heart of Lie theory.
This book contains the proceedings of the 2012–2014 Southeastern Lie Theory Workshop Series held at North Carolina State University in April 2012, at College of Charleston in December 2012, at Louisiana State University in May 2013, and at University of Georgia in May 2014. Some of the articles by experts in the field survey recent developments while others include new results in representations of Lie algebras, and quantum groups, vertex (operator) algebras and Lie superalgebras.
The Category of Graded Rings.- The Category of Graded Modules.- Modules over Stronly Graded Rings.- Graded Clifford Theory.- Internal Homogenization.- External Homogenization.- Smash Products.- Localization of Graded Rings.- Application to Gradability.- Appendix A:Some Category Theory.- Appendix B: Dimensions in an abelian Category.- Bibliography.- Index.-
This is an essentially self-contained monograph centered on the new double Hecke algebra technique.
This reprint of a 1983 Yale graduate course makes results in modular representation theory accessible to an audience ranging from second-year graduate students to established mathematicians. Following a review of background material, the lectures examine three closely connected topics in modular representation theory of finite groups: representations rings; almost split sequences and the Auslander-Reiten quiver; and complexity and cohomology varieties, which has become a major theme in representation theory.