Related papers: The Chamber Ansatz for quantum unipotent cells

Using mirror symmetry as described by Hori and Vafa, we compute the quantum equivariant cohomology ring of toric manifolds. This ring arises naturally in topological gauged sigma-models and is related to the Hamiltonian Gromov-Witten…

A brief exposition of the general theory of characteristic classes of quantum principal bundles is given. The theory of quantum characteristic classes incorporates ideas of classical Weil theory into the conceptual framework of…

We conjecture that the complex of Soergel bimodules associated with the full twist braid is categorically diagonalizable, for any finite Coxeter group. This utilizes the theory of categorical diagonalization introduced earlier by the…

We prove that the ideal of relations in the (equivariant) quantum K ring of a homogeneous space is generated by quantizations of each of the generators of the ideal in the classical (equivariant) K ring. This extends to quantum K theory a…

In [J14], a conjecture was proposed on a relation between the global Arthur parameters and the structure of Fourier coefficients of the automorphic representations in the corresponding global Arthur packets. In this paper, we discuss the…

In quantum mechanics, often it is important for the representation of quantum system to study the structure-preserving bijective maps of the quantum system. Such maps are also called isomorphisms or automorphisms. In this note, using the…

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…

We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space. We give a necessary and sufficient condition so that the…

Let $K$ be a field of characteristic two, and let $\lambda$ be a two-part partition of some natural number $r$. Denote the permutation module corresponding to the (maximal) Young subgroup $\Sigma_\lambda$ in $\Sigma_r$ by $M^\lambda$. We…

In this article, we construct new derived autoequivalences of generalised Kummer varieties. Together with Huybrechts-Thomas twists around $\mathbb{P}^n$-objects, these are the only known examples of such symmetries.

We describe an attempt to make quantum K-theory (of stable maps) more amenable to the self-duality/rigidity arguments of arXiv:1512.07363 in quasimap theory, by twisting the virtual structure sheaf. For $\mathbb{P}^n$ this twist produces…

A universal quantum gate is introduced for tensors of vector spaces. By using integer powers of such a gate and by using classical reversible gates one can approximate any element of the unitary group to any accuracy needed. The proof uses…

We show that quantum coherence can increase the quantum efficiency of various thermodynamic systems. For example, we can enhance the quantum efficiency for a quantum dot photocell, a laser based solar cell and the photo-Carnot quantum heat…

We show that the Baum-Connes morphism twisted by a non-unitary representation, defined in [GA08], is an isomorphism for a large class of groups satisfying the Baum-Connes conjecture. Such class contains all the real semi-simple Lie groups,…

We give local axioms that uniquely characterize the crystal-like structure on shifted tableaux developed in a previous paper by Gillespie, Levinson, and Purbhoo. These axioms closely resemble those developed by Stembridge for type A tableau…

We prove that every endomorphism of a simple quantum generalized Weyl algebra $A$ over a commutative Laurent polynomial ring in one variable is an automorphism. This is achieved by obtaining an explicit classification of all endomorphisms…

We show that any split extension of a right-angled Coxeter group $W_{\Gamma}$ by a generating automorphism of finite order acts faithfully and geometrically on a $\mathrm{CAT}(0)$ metric space.

The quantum baker map possesses two symmetries: a canonical "spatial" symmetry, and a time-reversal symmetry. We show that, even when these features are taken into account, the asymptotic entangling power of the baker's map does not always…

Let ${\mathfrak p}\subset {\mathfrak g}$ be a parabolic subalgebra of s simple finite dimensional Lie algebra over ${\mathbb C}$. To each pair $w^{\mathfrak a}\leq w^{\mathfrak c}$ of minimal left coset representatives in the quotient space…

We show that the set of totally positive unipotent lower-triangular Toeplitz matrices in $GL_n$ form a real semi-algebraic cell of dimension $n-1$. Furthermore we prove a natural cell decomposition for its closure. The proof uses properties…