# Nilpotent representations of classical quantum groups at roots of unity

## Abstract

Properly specializing the parameters in 'Schnizer modules', for types A,B,C, and D, we get its unique primitive vector. Then we show that the module generated by the primitive vector is an irreducible highest weight module of finite dimensional classical quantum groups at roots of unity.

- Authors:

- Department of Mathematics, Sophia University, Chiyoda-ku-Kioicho 7-1, Tokyo 102-8554 (Japan)

- Publication Date:

- OSTI Identifier:
- 20699622

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 46; Journal Issue: 11; Other Information: DOI: 10.1063/1.2107307; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; GROUP THEORY; IRREDUCIBLE REPRESENTATIONS; QUANTUM GROUPS; QUANTUM MECHANICS; VECTORS

### Citation Formats

```
Abe, Yuuki, and Nakashima, Toshiki.
```*Nilpotent representations of classical quantum groups at roots of unity*. United States: N. p., 2005.
Web. doi:10.1063/1.2107307.

```
Abe, Yuuki, & Nakashima, Toshiki.
```*Nilpotent representations of classical quantum groups at roots of unity*. United States. doi:10.1063/1.2107307.

```
Abe, Yuuki, and Nakashima, Toshiki. Tue .
"Nilpotent representations of classical quantum groups at roots of unity". United States.
doi:10.1063/1.2107307.
```

```
@article{osti_20699622,
```

title = {Nilpotent representations of classical quantum groups at roots of unity},

author = {Abe, Yuuki and Nakashima, Toshiki},

abstractNote = {Properly specializing the parameters in 'Schnizer modules', for types A,B,C, and D, we get its unique primitive vector. Then we show that the module generated by the primitive vector is an irreducible highest weight module of finite dimensional classical quantum groups at roots of unity.},

doi = {10.1063/1.2107307},

journal = {Journal of Mathematical Physics},

number = 11,

volume = 46,

place = {United States},

year = {Tue Nov 01 00:00:00 EST 2005},

month = {Tue Nov 01 00:00:00 EST 2005}

}

DOI: 10.1063/1.2107307

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