# Affine Kac-Moody symmetric spaces related with A{sub 1}{sup (1)}, A{sub 2}{sup (1)}, A{sub 2}{sup (2)}

## Abstract

Symmetric spaces associated with Lie algebras and Lie groups which are Riemannian manifolds have recently got a lot of attention in various branches of Physics for their role in classical/quantum integrable systems, transport phenomena, etc. Their infinite dimensional counter parts have recently been discovered which are affine Kac-Moody symmetric spaces. In this paper we have (algebraically) explicitly computed the affine Kac-Moody symmetric spaces associated with affine Kac-Moody algebras A{sub 1}{sup (1)},A{sub 2}{sup (1)},A{sub 2}{sup (2)}. We hope these types of spaces will play similar roles as that of symmetric spaces in many physical systems.

- Authors:

- Department of Mathematics, National Institute of Technology Rourkela, Rourkela 769008, Odisha (India)

- Publication Date:

- OSTI Identifier:
- 22306075

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; LIE GROUPS; MATHEMATICAL MANIFOLDS; MATHEMATICAL SPACE; QUANTUM MECHANICS; RIEMANN SPACE; SYMMETRY

### Citation Formats

```
Nayak, Saudamini, E-mail: anumama.nayak07@gmail.com, and Pati, K. C., E-mail: kcpati@nitrkl.ac.in.
```*Affine Kac-Moody symmetric spaces related with A{sub 1}{sup (1)}, A{sub 2}{sup (1)}, A{sub 2}{sup (2)}*. United States: N. p., 2014.
Web. doi:10.1063/1.4889796.

```
Nayak, Saudamini, E-mail: anumama.nayak07@gmail.com, & Pati, K. C., E-mail: kcpati@nitrkl.ac.in.
```*Affine Kac-Moody symmetric spaces related with A{sub 1}{sup (1)}, A{sub 2}{sup (1)}, A{sub 2}{sup (2)}*. United States. doi:10.1063/1.4889796.

```
Nayak, Saudamini, E-mail: anumama.nayak07@gmail.com, and Pati, K. C., E-mail: kcpati@nitrkl.ac.in. Fri .
"Affine Kac-Moody symmetric spaces related with A{sub 1}{sup (1)}, A{sub 2}{sup (1)}, A{sub 2}{sup (2)}". United States.
doi:10.1063/1.4889796.
```

```
@article{osti_22306075,
```

title = {Affine Kac-Moody symmetric spaces related with A{sub 1}{sup (1)}, A{sub 2}{sup (1)}, A{sub 2}{sup (2)}},

author = {Nayak, Saudamini, E-mail: anumama.nayak07@gmail.com and Pati, K. C., E-mail: kcpati@nitrkl.ac.in},

abstractNote = {Symmetric spaces associated with Lie algebras and Lie groups which are Riemannian manifolds have recently got a lot of attention in various branches of Physics for their role in classical/quantum integrable systems, transport phenomena, etc. Their infinite dimensional counter parts have recently been discovered which are affine Kac-Moody symmetric spaces. In this paper we have (algebraically) explicitly computed the affine Kac-Moody symmetric spaces associated with affine Kac-Moody algebras A{sub 1}{sup (1)},A{sub 2}{sup (1)},A{sub 2}{sup (2)}. We hope these types of spaces will play similar roles as that of symmetric spaces in many physical systems.},

doi = {10.1063/1.4889796},

journal = {Journal of Mathematical Physics},

number = 8,

volume = 55,

place = {United States},

year = {Fri Aug 15 00:00:00 EDT 2014},

month = {Fri Aug 15 00:00:00 EDT 2014}

}

DOI: 10.1063/1.4889796

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