A combinatorial formula for affine Hall–Littlewood functions via a weighted Brion theorem

Feigin, Boris; Makhlin, Igor

doi:10.1007/s00029-016-0223-4

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2018

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“…This degeneration changes combinatorial structure, in particular, some of the vertices merge. But one can ignore this when using Brion theorem (see arguments in [18,Sec. 8]).…”

Section: 4mentioning

confidence: 99%

Plane partitions with a “pit”: generating functions and representation theory

Bershtein

Feigin

Merzon

2018

Sel. Math. New Ser.

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We study plane partitions satisfying condition a n+1,m+1 = 0 (this condition is called "pit") and asymptotic conditions along three coordinate axes. We find the formulas for generating function of such plane partitions.Such plane partitions label the basis vectors in certain representations of quantum toroidal gl 1 algebra, therefore our formulas can be interpreted as the characters of these representations. The resulting formulas resemble formulas for characters of tensor representations of Lie superalgebra gl m|n . We discuss representation theoretic interpretation of our formulas using q-deformed W -algebra gl m|n .1 Usually a formula is called bosonic if it equals a linear combination of characters of algebra of polynomials. In our case bosonic formula is a combination of terms q ∆ /(q) n+m ∞ .

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“…This degeneration changes combinatorial structure, in particular, some of the vertices merge. But one can ignore this when using Brion theorem (see arguments in [18,Sec. 8]).…”

Section: 4mentioning

confidence: 99%