We describe new Banach (not C∗ !) algebras generated by Toeplitz operators which are commutative on each weighted Bergman space over the unit ball B, where n > 2. For n = 2 all these algebras collapse to the single C∗-algebra generated by Toeplitz operators with quasi-parabolic symbols. As a by-product, we describe the situations when the product of mutually commuting Toeplitz operators is a To...

The natural su(N) generalization of the XX model is introduced and analyzed. It is defined in terms of the characterizing properties of the usual XX model: the existence of two infinite sequences of mutually commuting conservation laws and the existence of two infinite sequences of mastersymmetries. The integrability of these models, which cannot be obtained in a degenerate limit of the su(N)-X...

Abstract Let G be a compact connected Lie group, and let $\operatorname {Hom}({\mathbb {Z}}^m,G)$ the space of pairwise commuting m -tuples in . We study problem which primes $p \operatorname {Z}}^m,G)_1$ , component containing element $(1,\ldots ,1)$ has p -torsion homology. will prove that for $m\ge 2$ homology if only divides order Weyl group $G=SU(n)$ some exceptional groups. also compute t...

Using the spectral subspaces obtained in [HS], Brown’s results (cf. [Bro]) on the Brown measure of an operator in a type II1 factor (M, τ) are generalized to finite sets of commuting operators in M. It is shown that whenever T1, . . . , Tn ∈ M are mutually commuting operators, there exists one and only one compactly supported Borel probability measure μT1,...,Tn on B(C) such that for all α1, . ...

This paper concerns the enumeration of simultaneous conjugacy classes [Formula: see text]-tuples commuting matrices in upper triangular group text] and unitriangular over finite field odd characteristic. is done for text], by computing branching rules. Further, using matrix thus computed, we explicitly get probabilities each case.

We investigate local conserved charges in principal chiral models in 1+1 dimensions. There is a classically conserved local charge for each invariant tensor of the underlying group. We prove that these are always in involution with the non-local Yangian charges and we study their classical Poisson bracket algebra. For the groups U(N), O(N) and Sp(N) we show that there are infinitely many commut...

A three-dimensional polynomial algebra of order m is defined by the commutation relations [P0, P±] = ±P±, [P+, P−] = φ (P0) where φ(P0) is an m-th order polynomial in P0 with the coefficients being constants or central elements of the algebra. It is shown that two given mutually commuting polynomial algebras of orders l and m can be combined to give two distinct (l + m + 1)-th order polynomial ...

We employ techniques from the theory of disintegration of measures to study the Lifting Problem for commuting n-tuples of subnormal weighted shifts. We obtain a new necessary condition for the existence of a lifting, and generate new pathology associated with bringing together the Berger measures associated to each individual weighted shift. For subnormal 2-variable weighted shifts, we then fin...

A directed BIB design DB(k, A; v) is a BIB design B(k, 2A; v) in which the blocks are transitively ordered k-tuples and each ordered pair of elements occurs in exactly A blocks. A nested directed BIB design NDB(k, A; v) of form IT2<n<k-l(njn, An)in is a DB(k, A; v) where each block contains E2<n<k-l injn mutually disjoint subblocks, injn subblocks of which are partitIoned into in mutually disjo...