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Teodor Banica

  1. Quantum automorphisms of twisted group algebras and free hypergeometric laws.

    Ср, 02/17/2010 - 16:01 — SomNambul
    Authors: Teodor Banica, Stephen Curran, Julien Bichon
    Subjects: Quantum Algebra
    Abstract

    We prove that we have an isomorphism of type $A_{aut}(\mathbb
    C_\sigma[G])\simeq A_{aut}(\mathbb C[G])^\sigma$, for any finite group $G$, and
    any 2-cocycle $\sigma$ on $G$. In the particular case $G=\mathbb Z_n^2$, this
    leads to a Haar-measure preserving identification between the subalgebra of
    $A_o(n)$ generated by the variables $u_{ij}^2$, and the subalgebra of
    $A_s(n^2)$ generated by the variables $X_{ij}=\sum_{a,b=1}^np_{ia,jb}$.

  2. Invariants of the half-liberated orthogonal group.

    Пт, 10/16/2009 - 17:25 — SomNambul
    Authors: Teodor Banica, Roland Vergnioux
    Subjects: Quantum Algebra
    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 for $O_n^*$, and a number of
    methods inspired from the theory of Lie algebras.

  3. Invariants of the half-liberated orthogonal group.

    Пт, 10/16/2009 - 17:25 — SomNambul
    Authors: Teodor Banica, Roland Vergnioux
    Subjects: Quantum Algebra
    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 for $O_n^*$, and a number of
    methods inspired from the theory of Lie algebras.

  4. On polynomial integrals over the orthogonal group.

    Чт, 10/08/2009 - 10:54 — SomNambul
    Authors: Jean-Marc Schlenker, Teodor Banica, Benoit Collins
    Subjects: Mathematical Physics
    Abstract

    We consider integrals of type $\int_{O_n}u_{11}^{a_1}...
    u_{1n}^{a_n}u_{21}^{b_1}... u_{2n}^{b_n} du$, with respect to the Haar measure
    on the orthogonal group. We establish several remarkable invariance properties
    satisfied by such integrals, by using combinatorial methods. We present as well
    a general formula for such integrals, as a sum of products of factorials.

  5. Stochastic aspects of easy quantum groups.

    Ср, 09/02/2009 - 12:02 — SomNambul
    Authors: Teodor Banica, Stephen Curran, Roland Speicher
    Subjects: Operator Algebras
    Abstract

    We consider several orthogonal quantum groups satisfying the easiness
    assumption axiomatized in our previous paper. For each of them we discuss the
    computation of the asymptotic law of Tr(u^k) with respect to the Haar measure,
    u being the fundamental representation. For the classical groups O_n, S_n we
    recover in this way some well-known results of Diaconis and Shahshahani.

  6. Stochastic aspects of easy quantum groups.

    Ср, 09/02/2009 - 12:02 — SomNambul
    Authors: Teodor Banica, Stephen Curran, Roland Speicher
    Subjects: Operator Algebras
    Abstract

    We consider several orthogonal quantum groups satisfying the easiness
    assumption axiomatized in our previous paper. For each of them we discuss the
    computation of the asymptotic law of Tr(u^k) with respect to the Haar measure,
    u being the fundamental representation. For the classical groups O_n, S_n we
    recover in this way some well-known results of Diaconis and Shahshahani.

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