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**1 - 5**of**5**### Multivariate quadratic transformations and the interpolation kernel

, 2014

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by Paul Zinn-justin

Venue: | IN KENJI IOHARA, SOPHIE MORIER-GENOUD AND BERTRAND RÉMY (EDS.), SYMMETRIES, INTEGRABLE SYSTEMS AND REPRESENTATIONS, VOL |

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by
Hjalmar Rosengren

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...braic differential equation for the functions T (k) n , see Theorem 3.3. Special cases of this equation have been obtained by Bazhanov and Mangazeev [BM1, MB] (without complete proof) and Zinn-Justin =-=[Z]-=-. An important application of the Schrödinger equation is that, when combined with minor relations for the determinants defining T (k) n , it can be used to derive bilinear relations for the polynomia...

by
Jasper Stokman, Bart Vlaar

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...r the XYZ spin chain or elliptic solid-on-solid models, is expected to lead to connections to elliptic hypergeometric functions [55, 64, 65, 66]. Only some first steps have been made here, see, e.g., =-=[78, 73]-=-. 1.6. Acknowledgements. We are grateful to P. Baseilhac, J. de Gier, B. Nienhuis, N. Reshetikhin and P. Zinn-Justin for stimulating discussions. The work of B.V. was supported by an NWO Free Competit...

by
Matteo Beccaria

"... staggered fermion chain with supersymmetry on open intervals ..."

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...appear also in the exact ground states of the XYZ spin chain along a special line of couplings, and are solutions to a non-linear recursion relations related to the Painlevé VI differential equation =-=[19, 20, 21]-=-. Further evidence for the connection between the staggered M1 model and the special XYZ chain was given [22]: in fact, their Hamiltonians have coinciding spectra in several momentum subsectors. In th...

by
Eric M. Rains
, 2014

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... ±1 j ) (6.45) = [ ∏ 1≤i,j≤n θp(p 1/3x±1i x ±1 n+j)∏ 1≤i<j≤n x −1 i x −1 n+1θp(xixj , xi/xj , xn+ixn+j , xn+i/xn+j) det 1≤i,j≤n 1 θp(p1/3x ±1 i x ±1 n+j) ]2 . (Some similar factorizations appeared in =-=[29]-=-, but the above appears to be new.) This is, in a somewhat disguised way, a special case of the more general identity ∏ 1≤i<j≤2n zi − zj yi − yj pf1≤i,j≤2n (yi − yj)2 zi − zj = [ ∏ 1≤i,j≤n (zi − zn+j)...

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