Differential Operators And Highest Weight Representations download pdf
Differential Operators And Highest Weight Representations. Mark G. Davidson
- Author: Mark G. Davidson
- Published Date: 01 Nov 1991
- Publisher: American Mathematical Society
- Language: English
- Format: Paperback
- ISBN10: 0821825097
- ISBN13: 9780821825099
- Filename: differential-operators-and-highest-weight-representations.pdf
- Dimension: 171.45x 247.65x 6.35mm::204.12g
Book Details:
Highest weight modules over the Lie algebra of differential operators on the circle W-algebras and other current algebras and their representations [See also Raising and Lowering Operators In Quantum Mechanics, can start with state jJ;J z= Jiand construct all other states of same Jusing lowering operator J Similarly with Isopsin, if start with = jI = 1;I z iand construct 0 and using lowering operator If we introduce Most of these vertex operator representations constructed are irreducible (Theorems 2.2, 3.6, 4.4, 4.6). The character formulas of these representations follow easily. All irreducible vertex operator representations constructed in this paper are highest weight modules (Theorem 5.1), thus the isomorphisms between these modules are clear. 2. a covariant discussion of differential equations [10, 11]. It was then Verma modules are graded highest weight representations V(c, h) freely generated. Differential operators and highest weight representations / Mark G. Davidson, Thomas J. Enright, Ronald J. Stanke Davidson, Mark G., 1955- View online Buy Operators and Representation Theory: Canonical Models for Algebras of Operators Arising in Quantum Mechanics (Dover Books on Physics) on FREE SHIPPING on Pris: 349 kr. E-bok. Laddas ned direkt. Köp Differential Operators and Highest Weight Representations av Mark G Davidson på. We determine the exchange relations of the level-one q-vertex operators of the quantum affine superalgebra Uq[gl(N| N)]. We study in detail the level-one irreducible highest weight representations where +(G) is the semigroup of dominant weights of G and k[X] is the sum of all irreducible. G-submodules in k[V ] with the highest weight Definition 1. We classify the irreducible quasifinite highest weight representations of the D of differential operators on the circle, is the most fundamental among these The second is the highest weight representations of the Lie algebra gℓ of infinite matrices, along with their applications to the theory of soliton equations, discovered Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary highest weight representations of the current (= affine Kac Moody) algebras. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We determine the exchange relations of the level-one q-vertex operators of the quantum affine superalgebra Uq [ gl(N|N)]. We study in details the level-one irreducible highest weight representations of Uq [ gl(2|2)], and compute the characters and supercharacters associated with these irreducible modules. Differential operator, In mathematics, any combination of derivatives applied to a function. It takes the form of a polynomial of derivatives, such as D2xx D2xy D2yx, where D2 is a second derivative and the subscripts indicate partial derivatives. Special differential operators include the Differential Operators and D-modules. 10. 5. Whose sheaf cohomology groups realize every highest weight representation. Let G be a This work concerns the representation theory of semisimple Lie groups. From the algebraic perspective, the theory of unitarizable highest weight modules is We study the level-one irreducible highest weight representations of U q [gl (1|1)] and associated q-vertex operators.We obtain the exchange relations satisfied these vertex operators. The characters and supercharacters associated with these irreducible representations are calculated 1. 1 (Twisted) Differential operators and D-modules. Any z z acts on any highest weight representation with highest weight HC(z)( + ). of G-invariant differential operators on G/K. This algebra is commutative. A spherical is the character of the representation of GL(n,C) with highest weight m. 3.16 Highest weight representations of semisimple Lie algebras Verma modules. Weyl character formula. 3.17 Induced representations 3.18 Unitary Representations of the Lorentz and Poincar e groups 3.19 Representations of supersymmetry algebras 3.20 Nonlinear sigma models: Quantum eld theories de ned group mani-folds and homogeneous spaces.
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