Related papers: Twisting the quantum grassmannian
The aim of this note is to show that the cycle decomposition of elements of the symmetric group admits a quite natural formulation in the framework of dual Coxeter theory, yielding a generalization of it to the family of so-called parabolic…
We quantize the Alekseev-Meinrenken solution r to the classical dynamical Yang-Baxter equation, associated to a Lie algebra g with an element t in S^2(g)^g. Namely, we construct a dynamical twist J with nonabelian base in the sense of P.…
We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref.[1]. The relevant ensembles of Hamiltonians are those…
We develop vertex and factorisation algebra analogues of the theory of quasitriangular bialgebras. Analogously to the classical theory, we prove their categories of representations are controlled by spectral R-matrices. In the vertex…
An operator space analysis of quantum stochastic cocycles is undertaken. These are cocycles with respect to an ampliated CCR flow, adapted to the associated filtration of subspaces, or subalgebras. They form a noncommutative analogue of…
We analyze within a semiclassical approximation the form factor for the fluctuations of quantum matrix elements around their classical average. We find two contributions: one is proportional to the form factor for the density of states,…
In this paper we introduce a kind of "noncommutative neighbourhood" of a semiclassical parameter corresponding to the Planck constant. This construction is defined as a certain filtered and graded algebra with an infinite number of…
We extend the classical result asserting that the twisting operator preserves certain Deligne--Lusztig character values for truncated formal power series; along the way we discuss some properties of centralisers. This leads us to the…
In this paper, we introduce quantum Demazure--Lusztig operators acting by ring automorphisms on the equivariant quantum cohomology of the Springer resolution. Our main application is a presentation of the torus-equivariant quantum…
The role of quantum universal enveloping algebras of symmetries in constructing a noncommutative geometry of space-time and corresponding field theory is discussed. It is shown that in the framework of the twist theory of quantum groups,…
Let q be a nonzero complex number that is not a root of unity. We give a criterion for (0) to be a primitive ideal of the algebra O_q(M_{m,n}) of quantum matrices. Next, we describe all height one primes of O_q(M_{m,n}); these two problems…
Let $K$ be a Gorenstein noetherian ring of finite Krull dimension, and consider the category of cohomologically noetherian commutative differential graded rings $A$ over $K$, such that $H^0(A)$ is essentially of finite type over $K$, and…
The aim of this article is to give explicit formulae for various generating functions, including the generating function of torus-invariant primitive ideals in the big cell of the quantum minuscule grassmannian of type B_n.
Let C be a coalgebra and consider the Grothendieck groups of the categories of the socle-finite injective right and left C-comodules. One of the main aims of the paper is to study Coxeter transformation, and its dual, of a pointed sharp…
This paper explores the orbit structure and homomesy (constant averages over orbits) properties of certain actions of toggle groups on the collection of independent sets of a path graph. In particular we prove a generalization of a homomesy…
We investigate the spectral and dynamical properties of a quantum particle constrained on a ring threaded by a magnetic flux in presence of a complex (non-Hermitian) potential. For a static magnetic flux, the quantum states of the particle…
Let $(W,S)$ be any Coxeter system and let $w \mapsto w^*$ be an involution of $W$ which preserves the set of simple generators $S$. Lusztig and Vogan have shown that the corresponding set of twisted involutions (i.e., elements $w \in W$…
We describe a construction of cocyclic perturbations of the semigroup of shifts on the semiaxis by means of the theory of model spaces. It is shown that one can choose an inner function that determines the model space so that the elements…
An element of a Coxeter group $W$ is fully commutative if any two of its reduced decompositions are related by a series of transpositions of adjacent commuting generators. These elements were extensively studied by Stembridge, in particular…
Our account of the problem of the classical limit of quantum mechanics involves two elements. The first one is self-induced decoherence, conceived as a process that depends on the own dynamics of a closed quantum system governed by a…