http://dspace.nbuv.gov.ua:80/handle/123456789/146038 2026-04-16T19:26:51Z http://dspace.nbuv.gov.ua:80/handle/123456789/147165 A Classical Limit of Noumi's q-Integral Operator Borodin, A.; Corwin, I.; Remenik, D. We demonstrate how a known Whittaker function integral identity arises from the t=0 and q→1 limit of the Macdonald polynomial eigenrelation satisfied by Noumi's q-integral operator. 2015-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/147164 Multispecies Weighted Hurwitz Numbers Harnad, J. The construction of hypergeometric 2D Toda τ-functions as generating functions for weighted Hurwitz numbers is extended to multispecies families. Both the enumerative geometrical significance of multispecies weighted Hurwitz numbers, as weighted enumerations of branched coverings of the Riemann sphere, and their combinatorial significance in terms of weighted paths in the Cayley graph of Sn are derived. The particular case of multispecies quantum weighted Hurwitz numbers is studied in detail. 2015-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/147163 Tableau Formulas for One-Row Macdonald Polynomials of Types Cn and Dn Feigin, B.; Hoshino, A.; Noumi, M.; Shibahara, J.; Shiraishi, J. We present explicit formulas for the Macdonald polynomials of types Cn and Dn in the one-row case. In view of the combinatorial structure, we call them ''tableau formulas''. For the construction of the tableau formulas, we apply some transformation formulas for the basic hypergeometric series involving very well-poised balanced ₁₂W₁₁ series. We remark that the correlation functions of the deformed W algebra generators automatically give rise to the tableau formulas when we principally specialize the coordinate variables. 2015-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/147162 Slavnov and Gaudin-Korepin Formulas for Models without U(1) Symmetry: the Twisted XXX Chain Belliard, S.; Pimenta, R.A. We consider the XXX spin-1/2 Heisenberg chain on the circle with an arbitrary twist. We characterize its spectral problem using the modified algebraic Bethe anstaz and study the scalar product between the Bethe vector and its dual. We obtain modified Slavnov and Gaudin-Korepin formulas for the model. Thus we provide a first example of such formulas for quantum integrable models without U(1) symmetry characterized by an inhomogenous Baxter T-Q equation. 2015-01-01T00:00:00Z