Invariants of the half-liberated orthogonal group

Teodor Banica[1]; Roland Vergnioux[2]

  • [1] Université de Toulouse 3 Département de Mathématiques 118, route de Narbonne 31062 Toulouse (France)
  • [2] Université de Caen Département de Mathématiques BP 5186 14032 Caen Cedex (France)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 6, page 2137-2164
  • ISSN: 0373-0956

Abstract

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The half-liberated orthogonal group O n * appears as intermediate quantum group between the orthogonal group O n , and its free version O n + . We discuss here its basic algebraic properties, and we classify its irreducible representations. The classification of representations is done by using a certain twisting-type relation between O n * and U n , a non abelian discrete group playing the role of weight lattice, and a number of methods inspired from the theory of Lie algebras. We use these results for showing that the dual discrete quantum group has polynomial growth.

How to cite

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Banica, Teodor, and Vergnioux, Roland. "Invariants of the half-liberated orthogonal group." Annales de l’institut Fourier 60.6 (2010): 2137-2164. <http://eudml.org/doc/116328>.

@article{Banica2010,
abstract = {The half-liberated orthogonal group $O_n^*$ appears as intermediate quantum group between the orthogonal group $O_n$, and its free version $O_n^+$. We discuss here its basic algebraic properties, and we classify its irreducible representations. The classification of representations is done by using a certain twisting-type relation between $O_n^*$ and $U_n$, a non abelian discrete group playing the role of weight lattice, and a number of methods inspired from the theory of Lie algebras. We use these results for showing that the dual discrete quantum group has polynomial growth.},
affiliation = {Université de Toulouse 3 Département de Mathématiques 118, route de Narbonne 31062 Toulouse (France); Université de Caen Département de Mathématiques BP 5186 14032 Caen Cedex (France)},
author = {Banica, Teodor, Vergnioux, Roland},
journal = {Annales de l’institut Fourier},
keywords = {Quantum group; maximal torus; root system; quantum group},
language = {eng},
number = {6},
pages = {2137-2164},
publisher = {Association des Annales de l’institut Fourier},
title = {Invariants of the half-liberated orthogonal group},
url = {http://eudml.org/doc/116328},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Banica, Teodor
AU - Vergnioux, Roland
TI - Invariants of the half-liberated orthogonal group
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 6
SP - 2137
EP - 2164
AB - The half-liberated orthogonal group $O_n^*$ appears as intermediate quantum group between the orthogonal group $O_n$, and its free version $O_n^+$. We discuss here its basic algebraic properties, and we classify its irreducible representations. The classification of representations is done by using a certain twisting-type relation between $O_n^*$ and $U_n$, a non abelian discrete group playing the role of weight lattice, and a number of methods inspired from the theory of Lie algebras. We use these results for showing that the dual discrete quantum group has polynomial growth.
LA - eng
KW - Quantum group; maximal torus; root system; quantum group
UR - http://eudml.org/doc/116328
ER -

References

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