N-point spherical functions and asymptotic boundary KZB equations

@article{Stokman2022NpointSF,
  title={N-point spherical functions and asymptotic boundary KZB equations},
  author={Jasper V. Stokman and Nicolai Reshetikhin},
  journal={Inventiones mathematicae},
  year={2022}
}
Let $G$ be a split real connected Lie group with finite center. In the first part of the paper we define and study formal elementary spherical functions. They are formal power series analogues of elementary spherical functions on $G$ in which the role of the quasi-simple admissible $G$-representations is replaced by Verma modules. For generic highest weight we express the formal elementary spherical functions in terms of Harish-Chandra series and integrate them to spherical functions on the… 
Trigonometric Real Form of the Spin RS Model of Krichever and Zabrodin
We investigate the trigonometric real form of the spin Ruijsenaars–Schneider system introduced, at the level of equations of motion, by Krichever and Zabrodin in 1995. This pioneering work and all
Bi-Hamiltonian structure of Sutherland models coupled to two u(n)* -valued spins from Poisson reduction
We introduce a bi-Hamiltonian hierarchy on the cotangent bundle of the real Lie group GL(n,C) , and study its Poisson reduction with respect to the action of the product group U(n) × U(n) arising
Pseudo-symmetric pairs for Kac-Moody algebras
Lie algebra involutions and their fixed-point subalgebras give rise to symmetric spaces and real forms of complex Lie algebras, and are well-studied in the context of symmetrizable KacMoody algebras.
Harmonic Analysis in d-Dimensional Superconformal Field Theory
Superconformal blocks and crossing symmetry equations are among central ingredients in any superconformal field theory. We review the approach to these objects rooted in harmonic analysis on the
Gaudin models and multipoint conformal blocks III: comb channel coordinates and OPE factorisation
Abstract We continue the exploration of multipoint scalar comb channel blocks for conformal field theories in 3D and 4D. The central goal here is to construct novel comb channel cross ratios that
Graphical calculus for quantum vertex operators, I: The dynamical fusion operator
. This paper is the first in a series on graphical calculus for quantum vertex operators. We establish in great detail the foundations of graphical calculus for ribbon categories and braided monoidal
Quantum Groups for Restricted SOS Models
We introduce the notion of restricted dynamical quantum groups through their category of representations, which are monoidal categories with a forgetful functor to the category of $\pi$-graded vector

References

SHOWING 1-10 OF 70 REFERENCES
SPHERICAL FUNCTIONS ON A SEMISIMPLE LIE GROUP.
  • Harish-Chandra
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1957
TLDR
It is shown that 7r2 is invariant under W, and therefore rS = e(8) r (s e W), where e(s) = ± 1 and 7r becomes a polynomial function.
Matrix Valued Spherical Functions Associated to the Complex Projective Plane
Abstract The main purpose of this paper is to compute all irreducible spherical functions on G=SU(3) of arbitrary type δ∈K, where K=S(U(2)×U(1))≃U(2). This is accomplished by associating to a
On the Plancherel Formula and the Paley-Wiener Theorem for Spherical Functions on Semisimple Lie Groups
One of the difficult points in the proof of Harish-Chandra's Plancherel formula for spherical functions on a semisimple Lie group is to show that an appropriate inversion formula exists for the
A Class of Calogero Type Reductions of Free Motion on a Simple Lie Group
The reductions of the free geodesic motion on a non-compact simple Lie group G based on the G+ × G+ symmetry given by left- and right-multiplications for a maximal compact subgroup $${G_{+} \subset
Generalized q-Onsager Algebras and Boundary Affine Toda Field Theories
Generalizations of the q-Onsager algebra are introduced and studied. In one of the simplest case and q = 1, the algebra reduces to the one proposed by Uglov–Ivanov. In the general case and q ≠ 1, an
Conformal blocks on elliptic curves and the Knizhnik-Zamolodchikov-Bernard equations
We give an explicit description of the vector bundle of WZW conformal blocks on elliptic curves with marked points as a subbundle of a vector bundle of Weyl group invariant vector valued theta
Symmetric pairs for Nichols algebras of diagonal type via star products
...
...