Fortieth Anniversary of Extremal Projector Method for Lie Symmetries

  title={Fortieth Anniversary of Extremal Projector Method for Lie Symmetries},
  author={Valeriy N. Tolstoy},
  journal={arXiv: Mathematical Physics},
  • V. Tolstoy
  • Published 23 December 2004
  • Mathematics
  • arXiv: Mathematical Physics
A brief review of the extremal projector method for Lie symme- tries (Lie algebras and superalgebras as well as their quantum analogs) is given. A history of its discovery and some simplest applications are presented. 

Extremal projectors for contragredient Lie (super)symmetries (short review)

A brief review of the extremal projectors for contragredient Lie (super)symmetries (finite-dimensional simple Lie algebras, basic classical Lie superalgebras, infinite-dimensional affine Kac-Moody

Extremal projectors for contragredient Lie (super)symmetries (short review)

A brief review of the extremal projectors for contragredient Lie (super)symmetries (finite-dimensional simple Lie algebras, basic classical Lie superalgebras, infinite-dimensional affine Kac-Moody

Mickelsson algebras and Zhelobenko operators

A rational theory for Clebsch-Gordan coefficients.

A theory of Clebsch-Gordan coefficients for $SL(2, C)$ is given using only rational numbers. Features include orthogonality relations, recurrence relations, and Regge's symmetry group. Results follow

Clebsch-Gordan coefficients for the Higgs algebra: The L\"{o}wdin-Shapiro approach

The L\"{o}wdin-Shapiro projection operator for the Higgs algebra is constructed and utilised to find an analytical expression for the Clebsch-Gordan coefficients for the same.

Functional approach to a Gelfand–Tsetlin-type basis for $$\mathfrak{o}_5$$

  • D. Artamonov
  • Mathematics
    Theoretical and Mathematical Physics
  • 2022
A realization of representations of the Lie algebra o 5 in the space of functions on a group Spin 5 ≃ Sp 4 is considered. In a representation we take a Gelfand-Tsetlin type base associated with a

Q A ] 1 1 Ju n 20 06 CPT-P 11-2006 ITEP-TH-13 / 06 Mickelsson algebras and Zhelobenko operators

We construct a family of automorphisms of Mickelsson algebra, satisfying braid group relations. The construction uses 'Zhelobenko cocycle' and includes the dynamical Weyl group action as a particular


. In the present paper we review the q -analog of the Quantum Theory of Angular Momenta based on the q -algebra su q (2), with an special emphasis on the representation of the Clebsch-Gordan

Ghost center and representations of the diagonal reduction algebra of $\mathfrak{osp}(1|2)$

. Reduction algebras are known by many names in the literature, including step alge- bras, Mickelsson algebras, Zhelobenko algebras, and transvector algebras, to name a few. These algebras, realized

The σ- Cohomology Analysis for Symmetric Higher-Spin Fields

In this paper, we present a complete proof of the so-called First On-Shell Theorem that determines dynamical content of the unfolded equations for free symmetric massless fields of arbitrary integer



Extremal Projectors and Generalized Mickelsson Algebras Over Reductive Lie Algebras

A description is given of "extremal projectors" in the associative envelopes of reductive (finite-dimensional) Lie algebras. In terms of extremal projectors, a description is then obtained of

Extremal Projectors of q-Boson Algebras

We define the extremal projector of the q-boson Kashiwara algebra and study their basic properties. Applying their properties to the representation theory of the category , whose objects are ‘‘upper

Projection operators and Clebsch-Gordan coefficients for the group SU3

Clebsch-Gordan coefficients of SU(3) with simple symmetry properties

Using an appropriate labelling operator constructed from representation generators, SU(3) Clebsch-Gordan coefficients are introduced whose symmetry properties are similar to those of their SU(2)

Extremal projector and universal R-matrix for quantized contragredient Lie (super)algebras

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Duality for Knizhnik–Zamolodchikov and Dynamical Equations

We consider the Knizhnik–Zamolodchikov (KZ) and dynamical equations, both differential and difference, in the context of (glk,gln) duality. We show that the KZ and dynamical equations naturally

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A modification of one of the defining relations of quantized Kac-Moody algebras, introduced by Drinfeld and Jimbo, is given. This modification allows one to extend the concept of quantized Kac-Moody

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It is shown that every finite-dimensional irreducible module over the general linear Lie superalgebragl(n/1) can be deformed to an irreducible module ofUq[gl(n/1)], aq-analogue of the universal

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1. The extremal projections of finite-dimensional contragredient Lie (super)-algebras ([11, [2]) provide a powerful and universal method for the solution of many problems in the representation theory

A Basis for Representations of Symplectic Lie Algebras

Abstract:A basis for each finite-dimensional irreducible representation of the symplectic Lie algebra ??(2n) is constructed. The basis vectors are expressed in terms of the Mickelsson lowering