Representation Theory of Lattice Current Algebras
نویسندگان
چکیده
منابع مشابه
Algebras Ii : Representation Theory
Representation theory is developed for the class of Galois algebras introduced recently by the authors. In particular, categories of Harish-Chandra modules are studied for integral Galois algebras which include generalized Weyl algebras, the universal enveloping algebra of gl n , the quantization and Yangians for gl 2 .
متن کاملRepresentation Theory of W-algebras
We study the representation theory of the W-algebra Wk(ḡ) associated with a simple Lie algebra ḡ at level k. We show that the “−” reduction functor is exact and sends an irreducible module to zero or an irreducible module at any level k ∈ C. Moreover, we show that the character of each irreducible highest weight representation of Wk(ḡ) is completely determined by that of the corresponding irred...
متن کاملRepresentation theory of Lie algebras
In these notes, we give a brief overview of the (finite dimensional) representation theory of finite dimensional semisimple Lie algebras. We first study the example of sl2(C) and then provide the general (additive) theory, along with an analysis of the representations of sl3(C). In the last section, we have a look at the multiplicative structure of the representation ring, discussing examples f...
متن کاملAn Application of Free Lie Algebras to Current Algebras and Their Representation Theory
We realize the current algebra of a Kac-Moody algebra as a quotient of a semi-direct product of the Kac-Moody Lie algebra and the free Lie algebra of the Kac-Moody algebra. We use this realization to study the representations of the current algebra. In particular we see that every ad-invariant ideal in the symmetric algebra of the Kac-Moody algebra gives rise in a canonical way to a representat...
متن کاملCluster algebras and representation theory
We apply the new theory of cluster algebras of Fomin and Zelevinsky to study some combinatorial problems arising in Lie theory. This is joint work with Geiss and Schröer (§3, 4, 5, 6), and with Hernandez (§8, 9). Mathematics Subject Classification (2000). Primary 05E10; Secondary 13F60, 16G20, 17B10, 17B37.
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: Communications in Mathematical Physics
سال: 1998
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s002200050260