# Fortieth Anniversary of Extremal Projector Method for Lie Symmetries

@article{Tolstoy2005FortiethAO, title={Fortieth Anniversary of Extremal Projector Method for Lie Symmetries}, author={Valeriy N. Tolstoy}, journal={arXiv: Mathematical Physics}, year={2005} }

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.

## 22 Citations

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

- Mathematics
- 2011

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)

- Mathematics
- 2010

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…

### A rational theory for Clebsch-Gordan coefficients.

- Mathematics
- 2017

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

- Mathematics
- 2012

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 $$\mathfrak{o}_5$$

- MathematicsTheoretical 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

- Mathematics
- 2006

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…

### ON THE q -ALGEBRA su q (2) AND ITS CONNECTION WITH THE QUANTUM THEORY OF ANGULAR MOMENTUM: A SURVEY

- Mathematics, Physics
- 2021

. 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 $\mathfrak{osp}(1|2)$

- Mathematics
- 2022

. 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

- MathematicsSymmetry
- 2021

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…

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