Quantum Toda chains intertwined
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- by A. Gerasimov, D. Lebedev and S. Oblezin
- St. Petersburg Math. J. 22 (2011), 411-435
- DOI: https://doi.org/10.1090/S1061-0022-2011-01149-5
- Published electronically: March 17, 2011
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Abstract:
An explicit construction of integral operators intertwining various quantum Toda chains is conjectured. Compositions of the intertwining operators provide recursive and $\mathcal {Q}$-operators for quantum Toda chains. In particular the authors’ earlier results on Toda chains corresponding to classical Lie algebras are extended to the generic $BC_n$- and Inozemtsev–Toda chains. Also, an explicit form of $\mathcal {Q}$-operators is conjectured for the closed Toda chains corresponding to the Lie algebras $B_{\infty }$, $C_{\infty }$, $D_{\infty }$, the affine Lie algebras $B^{(1)}_n$, $C^{(1)}_n$, $D^{(1)}_n$, $D^{(2)}_n$, $A^{(2)}_{2n-1}$, $A^{(2)}_{2n}$, and the affine analogs of $BC_n$- and Inozemtsev–Toda chains.References
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Bibliographic Information
- A. Gerasimov
- Affiliation: Institute for Theoretical and Experimental Physics, Moscow 117259, Russia; School of Mathematics, Trinity College, Dublin 2, Ireland; and Hamilton Mathematics Institute, Trinity College, Dublin 2, Ireland
- Email: anton@maths.tcd.ie
- D. Lebedev
- Affiliation: Institute for Theoretical and Experimental Physics, Moscow 117259, Russia
- Email: lebedev@itep.ru
- S. Oblezin
- Affiliation: Institute for Theoretical and Experimental Physics, Moscow 117259, Russia
- Email: Sergey.Oblezin@itep.ru
- Received by editor(s): January 11, 2010
- Published electronically: March 17, 2011
- Additional Notes: Supported by RFBR (grant nos. 08-01-00931-a and 09-01-93108-NCNIL-a). A. Gerasimov was also partly supported by a grant from Science Foundation Ireland. S. Oblezin gratefully acknowledges the support from Deligne’s 2004 Balzan prize in mathematics
- © Copyright 2011 American Mathematical Society
- Journal: St. Petersburg Math. J. 22 (2011), 411-435
- MSC (2010): Primary 81Q12
- DOI: https://doi.org/10.1090/S1061-0022-2011-01149-5
- MathSciNet review: 2729942
Dedicated: To Ludwig Dmitrievich Faddeev on the occasion of his 75th birthday \flushright The most convenient model for exploring such relationships is the Toda chain. L. D. Faddeev (Preprint LOMI, P-2-79) \endflushright