2 edition of **Generalized verma modules** found in the catalog.

Generalized verma modules

V. Mazorchuk

- 263 Want to read
- 29 Currently reading

Published
**2000**
by VNTL Publishers in Lviv, Ukraine
.

Written in English

- Representations of groups.,
- Verma modules.

**Edition Notes**

Includes bibliographical references.

Statement | V. Mazorchuk ; [editor, Michael Zarichnyi] |

Series | Mathematical studies -- v. 8 |

Contributions | Zarichnyi, M. |

The Physical Object | |
---|---|

Pagination | 182 p. |

Number of Pages | 182 |

ID Numbers | |

Open Library | OL21835484M |

ISBN 10 | 9667148904 |

Addeddate External-identifier urn:arXiv Identifier arxiv Identifier-ark ark://tvr5j Ocr ABBYY FineReader The Kazhdan-Lusztig conjecture for generalized Verma modules. Shelton, B.: Filtrations on generalized Verma modules for Hermitian symmetric pairs. J. für die Reine und Angew. Math. to appear L.G., Collingwood, D.H. The Kazhdan-Lusztig conjecture for generalized Verma modules. Math Z , – (). / Cited by:

We construct a generator system of the annihilator of a generalized Verma module of a classical reductive Lie algebra induced from a character of a parabolic subalgebra as an analogue of the minimal polynomial of a matrix. In a classical limit it gives a generator system of the defining ideal of any semisimple co-adjoint orbit of the Lie algebra. Categories of induced modules and their equivalence 53 The rough structure of generalized Verma modules: main results 55 References 56 1. Introduction The Weyl group acts via (exact) translation functors on the principal block of the Bernstein-Gelfand-Gelfand category O associated with a semi-simple complex.

MINIMAL POLYNOMIALS AND ANNIHILATORS OF GENERALIZED VERMA MODULES OF THE SCALAR TYPE HIROSHI ODA AND TOSHIO OSHIMA Abstract. We construct a generator system of the annihilator of a general-ized Verma module of a reductive Lie algebra induced from a character of a parabolic subalgebra as an analogue of the minimal polynomial of a matrix. 1. In this paper we give a sum formula for the radical filtration of generalized Verma modules in any (possibly singular) blocks of parabolic BGG category which can be viewed as a generalization of Jantzen sum formula for Verma modules in the usual BGG category O. Combined with Jantzen coefficients, we determine the radical filtrations for all basic generalized Verma modules.

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Generalized Verma modules could be used to prove a generalized Cartan- Melgason theorem was originally suggested by the apphcation of relative homo- logical algebra to the generalized Bernstein-Gelfand-GeKand resolution in [6(d)].

Generalized Verma modules are highest weight modules, and hence are quotients of Verma modules. The existence of a nonzero map between GVM's implies containment of the corresponding Verma modules; conversely, such an inclusion.

Generalized Verma and Wakimoto Modules. Smooth representation of afﬁne Kac-Moody algebrasGeneralized Verma ModulesGeneralized Wakimoto Modules What is a smooth representation. Let g[[t]]:= g bC[[t]]. Then tNg[[t]] is a subalgebra of g for all N 0. A module V over bg.

Generalized Verma modules, loop space cohomology and MacDonald-type identities J. Lepowsky. Annales scientifiques de l'École Normale Supérieure () Volume: 12, Issue: 2, page ; ISSN: ; Access Full Article top Access to full text Full (PDF) How to cite topCited by: An important class of modules over Lie algebras are the generalized Verma modules, which are one of the results of several di erent attempts to generalize the deep and rich theory of Verma modules.

Here, we shall only give a short introduction to Verma modules and then study generalized Verma modules in more detail. They are obtained.

Categorification of (induced) cell modules and the rough structure of generalized Verma modules by Volodymyr Mazorchuk, Catharina Stroppel, This paper presents categorifications of (right) cell modules and induced cell modules for Hecke algebras of finite Weyl groups.

Invariant operators and generalized Verma modules. Let U(g) resp. U(p) be the universal enveloping algebra of g resp. For each P-dominant weight µ, Vµ is also a representation of U(p) and we deﬁne the generalized Verma module Mp(µ):= U(g) ⊗U(p) Vµ where the left g-action is simply the left multiplication in U(g).

As a g−-module. Restrictions of generalized Verma modules to symmetric pairs Toshiyuki Kobayashi∗ Abstract We initiate a new line of investigation on branching problems for generalized Verma modules with respect to reductive symmetric pairs (g,g0).

In general, Verma modules may not contain any simple mod-ule when restricted to a reductive subalgebra. Restrictions of generalized Verma modules to symmetric pairs Article (PDF Available) in Transformation Groups volume 17(2):pp. June with 26 Reads How we measure 'reads'Author: Toshiyuki Kobayashi.

For a simple Lie algebra, L, over the complex numbers we study generalized Verma modules induced from modules which are torsion-free over a parabolic sub-algebra and the irreducible quotients of.

TY - JOUR AU - Collingwood, David H. AU - Casian, Luis G. TI - The Kazhdan-Lusztig Conjecture for Generalized Verma Modules JO - Mathematische Zeitschrift PY - VL - SP - EP - KW - enveloping algebra; semisimple Lie algebra; Hecke module; lower bound for dimension; Kazhdan-Lusztig conjecture; multiplicities; generalized Verma modules; regular integral infinitesimal character Cited by: Prominent objects in Op are the generalized Verma modules in the sense of J.

Lepowsky (=-=-=-). In defining a genuine p-adic counterpart of Op over Û(g) we build upon a certain weight theory for topological Fréchet modules over commutative Fréchet algebras (). Applying it to the Arens-Mic On the Support of Irreducible Weight Modules. Verma modules, named after Daya-Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics.

Verma modules can be used in the classification of irreducible representations of a complex semisimple Lie algebra. if you are looking to download the hc verma pdf than you are at place there below is a goolgle drive link for hc verma pdf of both volume 1 and volume 2 pdf., if you are a medical or engineering aspirant than you definitely know about this great book.

i.e HC verma 's concept of physics. Many iitian's and neet, AIIMS qualifiers recommend this. Restrictions of generalized Verma modules to symmetric pairs Toshiyuki Kobayashi Abstract We initiate a new line of investigation on branching problems for generalized Verma modules with respect to reductive symmetric pairs (g;g0).

In general, Verma modules may not contain any simple mod-ule when restricted to a reductive subalgebra. generalized Verma modules in any (possibly singular) blocks of parabolic BGG cat-egory Op. Our starting point is to develop an eﬃcient method to determine radical ﬁltrations of generalized Verma module with singularity.

The radical ﬁltrations of generalized Verma modules present critical information of related problems, such as. A class of generalized Verma modules over sl n + 2 are constructed from sl n + 1-modules which are U (h n)-free modules of rank 1.

The necessary and sufficient conditions for these sl n + 2 -modules to be simple are by: 1. H. Matumoto, The homomorphisms between scalar generalized Verma modules associated to maximal parabolic subalgebras, Duke Math.

Cited by: 3. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): this paper for all missing technical details. In particular, we define a generalization of the Shapovalov form on a GVM M(; p), see Chapter 5. We calculate the determinant of this form.

Using the determinant formula we generalize the BGG Theorem about the embeddings of GVMs. In the case when the semisimple part of the Levi factor of the parabolic subalgebra is isomorphic to sl(2, C) and the generalized Verma module is induced from an infinite-dimensional simple module, we prove that the associated Verma module is simple if and only if the original generalized Verma module Cited by: 9.

Matumoto, The homomorphisms between scalar generalized Verma modules associated to maximal parabolic subalgebras, Duke Math. J. () 75– Crossref, ISI, Google Scholar Author: Anthony C. Kable.Verma module vertex operator algebra VM(ℓΛ0), where Λ 0 is the fundamental weight of bg corresponding the aﬃne simple root α0.

In the present paper, we construct intertwining operators among generalized Verma mod-File Size: KB.Minimal polynomials and annihilators of generalized Verma modules of the scalar type Hiroshi Oda and Toshio Oshima Communicated by S.

Gindikin Abstract. We construct a generator system of the annihilator of a generalized Verma module of a reductive Cited by: