Related papers: Serre-Lusztig relations for $\imath$quantum groups…
Quantum isometry groups of spectral triples associated with approximately finite-dimensional C*-algebras are shown to arise as inductive limits of quantum symmetry groups of corresponding truncated Bratteli diagrams. This is used to…
A quantum theory is developed for a difference-difference system which can serve as a toy-model of the quantum Korteveg-de-Vries equation.
These notes are an introduction to the theory of quantum symmetries of finite and infinite sets, graphs, and locally compact spaces.
The article gives the second part of the treatise on Regular Algebraic $K$-theory (Sections V & VI) of the author. Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected to (but different from)…
We show a precise formula, in the form of a monomial, for certain families of parabolic Kazhdan-Lusztig polynomials of the symmetric group. The proof stems from results of Lapid-Minguez on irreducibility of products in the…
A theorem of Kazhdan and Lusztig establishes an equivalence between the category of G(CO)-integrable representations of the Kac-Moody algebra \hat{g}_{-\kappa} at a negative level -\kappa and the category \Rep_q(G) of (algebraic)…
In this paper, some left-symmetric algebras are constructed from linear functions. They include a kind of simple left-symmetric algebras and some examples appearing in mathematical physics. Their complete classification is also given, which…
The relativistic quantum mechanics equations for the electromagnetic interaction are propososed.
This is an introductory article for a mathematical definition of Coulomb branches of 3d N=4 SUSY gauge theories and geometric Satake correspondences for Kac-Moody Lie algebras based on Coulomb branches.
Kashiwara and Saito have a geometric construction of the infinity crystal for any symmetric Kac-Moody algebra. The underlying set consists of the irreducible components of Lusztig's quiver varieties, which are varieties of nilpotent…
Crystals which have a uniform distribution of defects are endowed with a Lie group description which allows one to construct an associated discrete structure. These structures are in fact the discrete subgroups of the ambient Lie group. The…
A symmetry extending the $T^2$-symmetry of the noncommutative torus $T^2_q$ is studied in the category of quantum groups. This extended symmetry is given by the quantum double-torus defined as a compact matrix quantum group consisting of…
Given a critical quantum spin chain with a microscopic Lie-group symmetry, corresponding e.g. to $U(1)$ or $SU(2)$ spin isotropy, we numerically investigate the emergence of Kac-Moody symmetry at low energies and long distances. In that…
We prove the solvability and nilpotency of Kac--Paljutkin's finite quantum group and Sekine quantum groups and we classify the solvable series of Kac--Paljutkin's finite quantum group via Cohen--Westreich's Burnside theorem. Some semisimple…
We establish a quantum Galois correspondence for compact Lie groups of automorphisms acting on a simple vertex operator algebra.
Complex manifolds with compatible metric have a naturally defined subspace of harmonic differential forms that satisfy Serre, Hodge, and conjugation duality, as well as hard Lefschetz duality. This last property follows from a…
Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected (but different from) group homology. It also gives a version of algebraic $K$-theory for rings by the simple functorial mapping assigning to…
We construct a relativistically covariant symmetry of QED. Previous local and nonlocal symmetries are special cases. This generalized symmetry need not be nilpotent, but nilpotency can be arranged with an auxiliary field and a certain…
The appearance of quantum groups in conformal field theories is traced back to the Poisson-Lie symmetries of the classical chiral theory. A geometric quantization of the classical theory deforms the Poisson-Lie symmetries to the quantum…
Recently, Lu and Wang formulated a Drinfeld type presentation for $\imath$quantum group $\widetilde{{\mathbf U}}^\imath$ arising from quantum symmetric pairs of split affine ADE type. In this paper, we generalize their results by…