Related papers: A field of quantum upper triangular matrices
We relate in a novel way the modular matrices of GKO diagonal cosets without fixed points to those of WZNW tensor products. Using this we classify all modular invariant partition functions of $su(3)_k\oplus su(3)_1/su(3)_{k+1}$ for all…
We discuss an approach to quantum gerbes over quantum groups in terms of q-deformation of transition functions for a loop group bundle. The case of the quantum group SUq(2) is treated in some detail.
We develop the theory of matroids over one-dimensional algebraic groups, with special emphasis on positive characteristic. In particular, we compute the Lindstr\"om valuations and Frobenius flocks of such matroids. Building on work by Evans…
For the special case of the quantum group $SL_q (2,{\bf C})\ (q= \exp \pi i/r,\ r\ge 3)$ we present an alternative approach to quantum gauge theories in two dimensions. We exhibit the similarities to Witten's combinatorial approach which is…
The Haar functional on the quantum $SU(2)$ group is the analogue of invariant integration on the group $SU(2)$. If restricted to a subalgebra generated by a self-adjoint element the Haar functional can be expressed as an integral with a…
We prove that an invariant subalgebra A_n^W of the Weyl algebra A_n is a Galois order over an adequate commutative subalgebra \Gamma when W is a two-parameters irreducible unitary reflection group G(m,1,n), m\geq 1, n\geq 1, including the…
We study the IIB matrix model in an interpretation where the matrices are differential operators defined on curved spacetimes. In this interpretation, coefficients of higher derivative operators formally appear to be massless higher spin…
There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…
We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional and including a Lagrangian formalism in which self-adjoint (Schroedinger) operators are…
We study N = 2 superconformal theories with gauge group SU(N) and 2N fundamental flavours in a locus of the Coulomb branch with a Z_N symmetry. In this special vacuum, we calculate the prepotential, the dual periods and the period matrix…
The quantum group analogue of the normalizer of SU(1,1) in SL(2,C) is an important and non-trivial example of a non-compact quantum group. The general theory of locally compact quantum groups in the operator algebra setting implies the…
We introduce a category of dual pairs of finite locally free algebras over a ring. This gives an efficient way to represent finite locally free commutative group schemes. We give a number of algorithms to compute with dual pairs of…
We present new additive results for the group invertibility in a ring. Then we apply our results to block operator matrices over Banach spaces and derive the existence of group inverses of $2\times 2$ block operator matrices. These…
The group algebras $kQ_{2^n}$ of the generalized quaternion groups $Q_{2^n}$ over fields $k$ which contain $\mathbb{F}_{2^{n-2}}$, are deformed to separable $k((t))$-algebras $[kQ_{2^n}]_t$. The dimensions of the simple components of…
We consider different variants of factorization of a 2x2 matrix Schroedinger/Pauli operator in two spatial dimensions. They allow to relate its spectrum to the sum of spectra of two scalar Schroedinger operators, in a manner similar to…
An extension of Quantum Group is described. We propose to unite the quantum groups with parameter q and with parameter modularly dual to q.
In this paper, we give an RTT presentation of the twisted quantum affine algebra of type $A_{2n-1}^{(2)}$ and show that it is isomorphic to the Drinfeld new realization via the Gauss decomposition of the L-operators. This provides the first…
In this paper we classify, up to isomorphism, the superinvolutions on algebras of upper block-triangular matrices over an algebraically closed field of characteristic different from $2$.
It was proved by Valenti and Zaicev, in 2011, that, if $G$ is an abelian group and $K$ is an algebraically closed field of characteristic zero, then any $G$-grading on the algebra of upper block triangular matrices over $K$ is isomorphic to…
Let $M$ be a four-holed sphere and $\Gamma$ the mapping class group of $M$ fixing $\partial M$. The group $\Gamma$ acts on the space ${\mathcal M}_{\mathcal B}(SU(2))$ of SU(2)-gauge equivalence classes of flat SU(2)-connections on $M$ with…