Heisenberg Idempotents on Unipotent Groups

Self-adjoint symmetry operators connected with the magnetic Heisenberg ring

In [1] we defined symmetry classes, commutation symmetries and symmetry operators in the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites and investigated them by means of tools from the representation theory of symmetric groups SN such as decompositions of ideals of the group ring C[SN ], idempotents of C[SN ], discrete Fourier transforms of SN , Littlewood-Richardson p...

Extensions and Covers for Semigroups Whose Idempotents Form a Left Regular Band

Proper extensions that are “injective on L-related idempotents” of R-unipotent semigroups, and much more generally of the class of generalised left restriction semigroups possessing the ample and congruence conditions, referred to here as glrac semigroups, are described as certain subalgebras of a λ-semidirect product of a left regular band by an R-unipotent or by a glrac semigroup, respectivel...

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

Central Extensions of Preprojective Algebras, the Quantum Heisenberg Algebra, and 2-dimensional Complex Reflection Groups

Preprojective algebras of quivers were introduced in 1979 by Gelfand and Ponomarev [GP], because for quivers of finite ADE type, they are models for indecomposable representations (they contain each indecomposable exactly once). Twenty years later, these algebras and their deformed versions introduced in [CBH] (for arbitrary quivers) became a subject of intense interest, since their representat...

Lattice Representations of Heisenberg Groups

This Heisenberg group is a 2-step nilpotent Lie group and is important in the study of toroidal compactifications of Siegel moduli spaces. In fact, H (g,h) R is obtained as the unipotent radical of the parabolic subgroup of Sp(g+h,R) associated with the rational boundary component Fg ( cf. [F-C] p. 123 or [N] p. 21 ). For the motivation of the study of this Heisenberg group we refer to [Y4]-[Y8...