Basics of representation theory Sample Clauses

Basics of representation theory for finite groups The concepts and results in this section can be found in most introductory text books on representation theory such as [70] and [31]. Let V be an R-module. A representation of a group G is a group homomorphism ρ : G → GL(V ). If V is free and of finite rank n over R then GL(V ) can be identified with GLn(R). The representation ρ gives V the structure of a (left) module of the group ring RG. Similarly any (left) RG-module defines a representation ρ given by ρ(g)v = g · v for all v ∈ V . Therefore we will refer to representations and RG-modules interchangeably. The degree of a representation ρ over a field F is the rank of the corresponding FG-module V . A representation ρ and its corresponding RG-module is called faithful if ρ is injective. We say that an RG-module V is simple, or its equivalent representation is irreducible, if it has no nontrivial RG-submodules. Furthermore we say V is semisimple if it can be written as direct sum of simple RG-submodules.
Sample 1Sample 2
AutoNDA by SimpleDocs

Related to Basics of representation theory

  • Rights of Representation Paragraph 1: At any level of the grievance procedure, at the grievant’s option the grievant shall be represented by the UTW, himself/herself, legal counsel or another person selected by the grievant. Provided, however, if an attorney is going to be present at a Level Two hearing for either the administration or UTW, the other side will be notified at least three (3) days prior to the hearing.

  • Breach of Representations, Etc Any representation, warranty, certification or other statement made or deemed made by any Credit Party in any Credit Document or in any statement or certificate at any time given by any Credit Party or any of its Subsidiaries in writing pursuant hereto or thereto or in connection herewith or therewith shall be false in any material respect as of the date made or deemed made; or

  • Scope of Representation The scope of representation shall be limited to matters relating to wages, hours of employment and other terms and conditions of employment as defined in Government Code Section 3543.2. Nothing herein may be construed to limit the right of the District to consult with CSEA on any matter outside of the scope of representation.

  • Breach of Representation Any representation or warranty made or deemed made by any Borrower or any Guarantor in this Agreement, any Other Document or any related agreement or in any certificate, document or financial or other statement furnished at any time in connection herewith or therewith shall prove to have been misleading in any material respect on the date when made or deemed to have been made;

  • Confirmation of Representations Borrower shall deliver, in connection with any Securitization, (a) one or more Officer’s Certificates certifying as to the accuracy of all representations made by Borrower in the Loan Documents as of the date of the closing of such Securitization in all relevant jurisdictions, and (b) certificates of the relevant Governmental Authorities in all relevant jurisdictions indicating the good standing and qualification of Mortgage Borrower, Senior Mezzanine Borrower, Borrower and Holdings as of the date of the Securitization.

  • Right of Representation An employee covered by this Agreement shall, under this Article, have the right to have an Association representative present at any time, subject to his requesting such representation.

  • Exclusivity of Representations The representations and warranties made by the Seller in this Agreement are the exclusive representations and warranties made by the Seller. The Seller hereby disclaims any other express or implied representations or warranties.

  • Breach of Representations In entering into this Agreement, Consultant acknowledges that County is materially relying on the representations, warranties, and certifications of Consultant stated in this article. County shall be entitled to recover any damages it incurs to the extent any such representation or warranty is untrue. In addition, if any such representation, warranty, or certification is false, County shall have the right, at its sole discretion, to terminate this Agreement without any further liability to Consultant, to deduct from the compensation due Consultant under this Agreement the full amount of any value paid in violation of a representation or warranty, and to recover all sums paid to Consultant under this Agreement. Furthermore, a false representation may result in debarment from County’s procurement activities.

  • Accuracy of Representations All of Buyer's representations and warranties in this Agreement (considered collectively), and each of these representations and warranties (considered individually), must have been accurate in all material respects as of the date of this Agreement and must be accurate in all material respects as of the Closing Date as if made on the Closing Date.

  • Letter of Representations Notwithstanding anything to the contrary in this Indenture or the Series Supplement, the parties hereto shall comply with the terms of each Letter of Representations applicable to such party.

Time is Money Join Law Insider Premium to draft better contracts faster.