TY - JOUR
T1 - A combinatorial formula for affine Hall–Littlewood functions via a weighted Brion theorem
AU - Feigin, Boris
AU - Makhlin, Igor
N1 - Publisher Copyright:
© 2016, Springer International Publishing.
PY - 2016/7/1
Y1 - 2016/7/1
N2 - We present a new combinatorial formula for Hall–Littlewood functions associated with the affine root system of type A~ n - 1, i.e., corresponding to the affine Lie algebra sl^ n. Our formula has the form of a sum over the elements of a basis constructed by Feigin, Jimbo, Loktev, Miwa and Mukhin in the corresponding irreducible representation. Our formula can be viewed as a weighted sum of exponentials of integer points in a certain infinite-dimensional convex polyhedron. We derive a weighted version of Brion’s theorem and then apply it to our polyhedron to prove the formula.
AB - We present a new combinatorial formula for Hall–Littlewood functions associated with the affine root system of type A~ n - 1, i.e., corresponding to the affine Lie algebra sl^ n. Our formula has the form of a sum over the elements of a basis constructed by Feigin, Jimbo, Loktev, Miwa and Mukhin in the corresponding irreducible representation. Our formula can be viewed as a weighted sum of exponentials of integer points in a certain infinite-dimensional convex polyhedron. We derive a weighted version of Brion’s theorem and then apply it to our polyhedron to prove the formula.
UR - http://www.scopus.com/inward/record.url?scp=84961207553&partnerID=8YFLogxK
U2 - 10.1007/s00029-016-0223-4
DO - 10.1007/s00029-016-0223-4
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AN - SCOPUS:84961207553
SN - 1022-1824
VL - 22
SP - 1703
EP - 1747
JO - Selecta Mathematica, New Series
JF - Selecta Mathematica, New Series
IS - 3
ER -