A symmetry reduction technique for higher order Painlev\'e systems

The symmetry reduction of higher order Painlev\'e systems is formulated in terms of Dirac procedure. A set of canonical variables that admit Dirac reduction procedure is proposed for Hamiltonian structures governing the ${A^{(1)}_{2M}}$ and ${A^{(1)}_{2M-1}}$ Painlev\'e systems for $M=2,3,...$.Comment: to appear in Phys. Lett.

The sixth Painleve equation arising from D_4^{(1)} hierarchy

The sixth Painleve equation arises from a Drinfel'd-Sokolov hierarchy associated with the affine Lie algebra of type D_4 by similarity reduction.Comment: 14 page

Nonsymmetric Askey-Wilson polynomials as vector-valued polynomials

Nonsymmetric Askey-Wilson polynomials are usually written as Laurent polynomials. We write them equivalently as 2-vector-valued symmetric Laurent polynomials. Then the Dunkl-Cherednik operator of which they are eigenfunctions, is represented as a 2x2 matrix-valued operator. As a new result made possible by this approach we obtain positive definiteness of the inner product in the orthogonality relations, under certain constraints on the parameters. A limit transition to nonsymmetric little q-Jacobi polynomials also becomes possible in this way. Nonsymmetric Jacobi polynomials are considered as limits both of the Askey-Wilson and of the little q-Jacobi case.Comment: 16 pages. Dedicated to Paul Butzer on the occasion of his 80th birthday. v4: minor correction in (4.14

Towards the solution of the Gn/Gp Puzzle in the Non-Mesonic Weak Decay of Lambda-Hypernuclei

One of the main open problems in the physics of Lambda-hypernuclei is the lack of a sound theoretical interpretation of the large experimental values for the ratio Gn/Gp=G(Lambda n -> nn)/G(Lambda p -> np). To approach the problem, we have incorporated a one-meson-exchange model for the Lambda N -> nN transition in finite nuclei in an intranuclear cascade code for the calculation of single and double-coincidence nucleon distributions corresponding to the non-mesonic weak decay of 5_Lambda-He and 12_Lambda-C. Due to the elimination of interferences, two-nucleon coincidences are expected to give a cleaner determination of Gn/Gp than single-nucleon observables. Single-nucleon distributions are found to be less sensitive to variations of Gn/Gp than double-coincidence spectra. The comparison of our results with preliminary KEK coincidence data allows us to extract a Gn/Gp ratio for 5_Lambda-He of 0.39+-0.11 when multinucleon induced channels are omitted.Comment: 12 RevTeX pages, 12 figure

Heisenberg realization for U_q(sln) on the flag manifold

We give the Heisenberg realization for the quantum algebra $U_q(sl_n)$, which is written by the $q$-difference operator on the flag manifold. We construct it from the action of $U_q(sl_n)$ on the $q$-symmetric algebra $A_q(Mat_n)$ by the Borel-Weil like approach. Our realization is applicable to the construction of the free field realization for the $U_q(\widehat{sl_n})$ [AOS].Comment: 10 pages, YITP/K-1016, plain TEX (some mistakes corrected and a reference added

Sigma Exchange in the Nonmesonic Decays of Light Hypernuclei and Violation of the Delta I=1/2 Rule

Nonmesonic weak decays of s-shell hypernuclei are analyzed in microscopic models for the Lambda N to NN weak interaction. A scalar-isoscalar meson, sigma, is introduced and its importance in accounting the decay rates, n/p ratios and proton asymmetry is demonstrated. Possible violation of the Delta I=1/2 rule in the nonmesonic weak decay of Lambda is discussed in a phenomenological analysis and several useful constraints are presented. The microscopic calculation shows that the current experimental data indicate a large violation of the Delta I=1/2 rule, although no definite conclusion can be derived due to large ambiguity of the decay rate of {^4_Lambda H}.Comment: 13 pages, 5 figure

Solutions to the ultradiscrete Toda molecule equation expressed as minimum weight flows of planar graphs

We define a function by means of the minimum weight flow on a planar graph and prove that this function solves the ultradiscrete Toda molecule equation, its B\"acklund transformation and the two dimensional Toda molecule equation. The method we employ in the proof can be considered as fundamental to the integrability of ultradiscrete soliton equations.Comment: 14 pages, 10 figures Added citations in v

Quasitriangular coideal subalgebras of Uq(g) in terms of generalized Satake diagrams

© 2020 The Authors. Bulletin of the London Mathematical Society is copyright © London Mathematical Society. This is an open access article under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits use, distribution and reproduction in any medium, provided the original work is properly cited.Let (Formula presented.) be a finite-dimensional semisimple complex Lie algebra and (Formula presented.) an involutive automorphism of (Formula presented.). According to Letzter, Kolb and Balagović the fixed-point subalgebra (Formula presented.) has a quantum counterpart (Formula presented.), a coideal subalgebra of the Drinfeld–Jimbo quantum group (Formula presented.) possessing a universal (Formula presented.) -matrix (Formula presented.). The objects (Formula presented.), (Formula presented.), (Formula presented.) and (Formula presented.) can all be described in terms of Satake diagrams. In the present work, we extend this construction to generalized Satake diagrams, combinatorial data first considered by Heck. A generalized Satake diagram naturally defines a semisimple automorphism (Formula presented.) of (Formula presented.) restricting to the standard Cartan subalgebra (Formula presented.) as an involution. It also defines a subalgebra (Formula presented.) satisfying (Formula presented.), but not necessarily a fixed-point subalgebra. The subalgebra (Formula presented.) can be quantized to a coideal subalgebra of (Formula presented.) endowed with a universal (Formula presented.) -matrix in the sense of Kolb and Balagović. We conjecture that all such coideal subalgebras of (Formula presented.) arise from generalized Satake diagrams in this way.Peer reviewe