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Representations of Lie algebras, quantum groups, and related topics : AMS Special Session, Representations of Lie Algebras, Quantum Groups, and Related Topics, November 12-13, 2016, North Carolina State University, Raleigh, North Carolina
This volume contains the proceedings of the AMS Special Session on Representations of Lie Algebras, Quantum Groups and Related Topics, held from November 12-13, 2016, at North Carolina State University, Raleigh, North Carolina.The articles cover various aspects of representations of Kac-Moody Lie algebras and their applications, structure of Leibniz algebras and Krichever-Novikov algebras, representations of quantum groups, and related topics.
eBook
Representations of Lie Algebras, Quantum Groups and Related Topics
This volume contains the proceedings of the AMS Special Session on Representations of Lie Algebras, Quantum Groups and Related Topics, held from November 12-13, 2016, at North Carolina State University, Raleigh, North Carolina. The articles cover various aspects of representations of Kac-Moody Lie algebras and their applications, structure of Leibniz algebras and Krichever-Novikov algebras, representations of quantum groups, and related topics.
eBook
Character identities in the twisted endoscopy of real reductive groups
Suppose G is a real reductive algebraic group, θ is an automorphism of G, and ω is a quasicharacter of the group of real points G(R). Under some additional assumptions, the theory of twisted endoscopy associates to this triple real reductive groups H. The Local Langlands Correspondence partitions the admissible representations of H(R) and G(R) into L-packets. The author proves twisted character identities between L-packets of H(R) and G(R) comprised of essential discrete series or limits of discrete series.
eBook
Affine Hecke algebras and quantum symmetric pairs
We introduce an affine Schur algebra via the affine Hecke algebra associated to Weyl group of affine type C. We establish
multiplication formulas on the affine Hecke algebra and affine Schur algebra. Then we construct monomial bases and canonical bases for
the affine Schur algebra. The multiplication formula allows us to establish a stabilization property of the family of affine Schur
algebras that leads to the modified version of an algebra
eBook
Cohomological Tensor Functors on Representations of the General Linear Supergroup
We define and study cohomological tensor functors from the category
eBook
Representations of algebraic groups, quantum groups, and Lie algebras : AMS-IMS-SIAM Joint Summer Research Conference, July 11-15, 2004, Snowbird Resort, Snowbird, Utah
The book contains several well-written, accessible survey papers in many interrelated areas of current research. These areas cover various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie super algebras. Geometric methods have been instrumental in representation theory, and these proceedings include surveys on geometric as well as combinatorial constructions of the crystal basis for representations of quantum groups. Humphreys' paper outlines intricate connections among irreducible representations of certain blocks of reduced enveloping algebras of semi-simple Lie algebras in positive characteristic, left cells in two sided cells of affine Weyl groups, and the geometry of the nilpotent orbits. All these papers provide the reader with a broad picture of the interaction of many different research areas and should be helpful to those who want to have a glimpse of current research involving representation theory.
eBook
Exotic Cluster Structures on $SL_{n}
This is the second paper in the series of papers dedicated to the study of natural cluster structures in the rings of regular functions on simple complex Lie groups and Poisson-Lie structures compatible with these cluster structures. According to our main conjecture, each class in the Belavin-Drinfeld classification of Poisson-Lie structures on \\mathcal{G} corresponds to a cluster structure in \\mathcal{O}(\\mathcal{G}). The authors have shown before that this conjecture holds for any \\mathcal{G} in the case of the standard Poisson-Lie structure and for all Belavin-Drinfeld classes in SL_n, n.
eBook
Representations of Lie Algebras
This bold and refreshing approach to Lie algebras assumes only modest prerequisites (linear algebra up to the Jordan canonical form and a basic familiarity with groups and rings), yet it reaches a major result in representation theory: the highest-weight classification of irreducible modules of the general linear Lie algebra. The author's exposition is focused on this goal rather than aiming at the widest generality and emphasis is placed on explicit calculations with bases and matrices. The book begins with a motivating chapter explaining the context and relevance of Lie algebras and their representations and concludes with a guide to further reading. Numerous examples and exercises with full solutions are included. Based on the author's own introductory course on Lie algebras, this book has been thoroughly road-tested by advanced undergraduate and beginning graduate students and it is also suited to individual readers wanting an introduction to this important area of mathematics.
eBook