Related papers: Holomorphy of normalized intertwining operators fo…
In this paper, we present several new structures for the colored HOMFLY-PT invariants of framed links. First, we prove the strong integrality property for the normalized colored HOMFLY-PT invariants by purely using the HOMFLY-PT skein…
The purpose of this paper is to generalize a very famous result on products of normal operators, due to I. Kaplansky. The context of generalization is that of bounded hyponormal and unbounded normal operators on complex separable Hilbert…
This exposition presents a self-contained proof of the $A_2$ theorem, the quantitatively sharp norm inequality for singular integral operators in the weighted space $L^2(w)$. The strategy of the proof is a streamlined version of the…
The Dunkl operators associated to a dihedral group are a pair of differential-difference operators that generate a commutative algebra acting on differentiable functions in $\mathbb{R}^2$. The intertwining operator intertwines between this…
In semiclassical holographic duality, the running couplings of a field theory are conventionally identified with the classical solutions of field equations in the dual gravitational theory. However, this identification is unclear when the…
For classical groups we show the isomorphism of the Knapp-Stein $R$-group, which describes the structure of parabolically induced representations, and the Arthur $R$-group of the parameter associated to the inducing representation by the…
The three equations named in the title are examples of infinite-dimensional completely integrable Hamiltonian systems, and are related to each other via simple geometric constructions. In this paper, these interrelationships are further…
We discuss how one calculates the coherent path integrals for locally interacting systems, where some inconsistencies with exact results have been reported previously. It is shown that the operator ordering subtlety that is hidden in the…
The entanglement theory in quantum systems with internal symmetries is rich due to the spontaneous creation of entangled pairs of charge/anti-charge particles at the entangling surface. We call these pair creation operators the bi-local…
We incorporate nonlinear covers of quasisplit reductive groups into the Langlands program, defining an L-group associated to such a cover. This L-group is an extension of the absolute Galois group of a local or global field $F$ by a complex…
We construct a unitary operator between Hilbert spaces of generalized eigenfunctions of Coulomb operators and the Laplace-Beltrami operator of hyperbolic space that intertwines their respective Poisson operators on $L^2(\mathbb{S}^{d-1})$.…
In this lecture we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. Our analysis is based on an approach to modular invariants using braided sector induction…
We construct interpolation operators for functions taking values in a symmetric space -- a smooth manifold with an inversion symmetry about every point. Key to our construction is the observation that every symmetric space can be realized…
To a maximal torus in a quasi-split semi-simple simply-connected group over a local field of characteristic 0, Langlands and Shelstad construct a cohomological invariant called the splitting invariant, which is an important component of…
The covariantization procedure is usually referred to the translation operator, that is the derivative. Here we introduce a general method to covariantize arbitrary differential operators, such as the ones defining the fundamental group of…
We present a finite algorithm for computing the set of irreducible unitary representations of a real reductive group G. The Langlands classification, as formulated by Knapp and Zuckerman, exhibits any representation with an invariant…
We present a novel approach for constructing quasi-isospectral higher-order Hamiltonians from time-independent Lax pairs by reversing the conventional interpretation of the Lax pair operators. Instead of treating the typically second-order…
We construct a version of kneading theory for families of monotonous functions on the real line. The generality of the setup covers two classical results from Milnor-Thurston's kneading theory: the first one is to dynamically characterise…
We prove that the linearization of a germ of holomorphic map of the type $F_\lambda(z)=\lambda(z+O(z^2))$ has a $ C^1$--holomorphic dependence on the multiplier $\lambda$. $C^1$--holomorphic functions are $ C^1$--Whitney smooth functions,…
Recently we propose a class of infinite-dimensional integral representations of classical gl(n+1)-Whittaker functions and local Archimedean local L-factors using two-dimensional topological field theory framework. The local Archimedean…