On q-Deformed $${{\mathfrak{gl}}_{\ell+1}}$$-Whittaker Function III
On q-Deformed $${{\mathfrak{gl}}_{\ell+1}}$$-Whittaker Function III
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关于 q 变形 $${{mathfrak{gl}}_{ell 1}}$$-Whittaker 函数 III
DOI：
10.1007/s11005-011-0468-y
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发表时间：
2011
影响因子：
1.2
通讯作者：
S. Oblezin
中科院分区：
文献类型：
--
作者：
A. Gerasimov;D. Lebedev;S. Oblezin
In this paper, we identify q-deformed $${\mathfrak{gl}_{\ell+1}}$$-Whittaker functions with a specialization of the Macdonald polynomials. This provides a representation of q-deformed $${\mathfrak{gl}_{\ell+1}}$$-Whittaker functions in terms of the Demazure characters of affine Lie algebra $${\widehat{\mathfrak{gl}}_{\ell+1}}$$. We also define a system of dual Hamiltonians for q-deformed $${\mathfrak{gl}_{\ell+1}}$$-Toda chains and give a new integral representation for the q-deformed $${\mathfrak{gl}_{\ell+1}}$$-Whittaker functions. Finally, we represent the q-deformed $${\mathfrak{gl}_{\ell+1}}$$-Whittaker function as a matrix element of a quantum torus algebra.
