scholarly journals Integrability criterion in terms of coprime property for the discrete Toda equation

2015 ◽  
Vol 56 (2) ◽  
pp. 022706 ◽  
Author(s):  
Masataka Kanki ◽  
Jun Mada ◽  
Tetsuji Tokihiro
Keyword(s):  
Toda Equation ◽  
Integrability Criterion

On the Full-Discrete Extended Generalised q-Difference Toda System

2017 ◽  
Vol 72 (8) ◽  
pp. 703-709
Author(s):  
Chuanzhong Li ◽  
Anni Meng
Keyword(s):  
Difference Equation ◽  
Hamiltonian Structure ◽  
Soliton Solutions ◽  
Toda Equation ◽  
Lax Pairs ◽  
Toda System ◽  
Toda Hierarchy

AbstractIn this paper, we construct a full-discrete integrable difference equation which is a full-discretisation of the generalised q-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of an extended generalised full-discrete q-Toda hierarchy are also constructed. To show the integrability, the bi-Hamiltonian structure and tau symmetry of the extended full-discrete generalised q-Toda hierarchy are given.

Square Integrable Representations and the Standard Module Conjecture for General Spin Groups

2009 ◽  
Vol 61 (3) ◽  
pp. 617-640 ◽  
Author(s):  
Wook Kim
Keyword(s):  
Half Plane ◽  
Spin Groups ◽  
Standard Module ◽  
Square Integrability ◽  
Integrability Criterion

Abstract.In this paper we study square integrable representations and L -functions for quasisplit general spin groups over a p-adic field. In the first part, the holomorphy of L -functions in a half plane is proved by using a variant formof Casselman's square integrability criterion and the Langlands–Shahidi method. The remaining part focuses on the proof of the standard module conjecture. We generalize Muić's idea via the Langlands–Shahidimethod towards a proof of the conjecture. It is used in the work of M. Asgari and F. Shahidi on generic transfer for general spin groups.

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