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Quantum cohomology of Hilb▫$_n({\mathbb C}^2)$▫ and the weighted hook walk on Young diagrams
Ciocan-Fontanine, Ionuţ ; Konvalinka, Matjaž ; Pak, Igor
Sledimo delom Okounkova in Pandharipandeja (2010), Diaconescuja in članku Ciocana-Fontaninea in drugih (v pripravi), ki študira ekvivariantno kvantno kohomologijo ▫$QH^\ast_{({\mathbb ...C}^\ast)^2}({\text{Hilb}}_n)$▫ Hilbertove sheme in relativne Donaldson-Thomasove teorije ▫${\mathbb P}^1 \times {\mathbb C}^2$▫, in pokažemo povezavo med ▫$J$▫-funkcijo Hilbertove sheme in kombinatorično identiteto z dvema spremenljivkama. To identiteto posplošimo na identiteto z več spremenljivkami, ki hkrati posplošuje tudi razmejitveno pravilo za dimenzije nerazcepnih upodobitev simetrične grupe za stopničasto particijo. Potem dokažemo to identiteto preko obtežene posplošitve sprehoda po kljukah Greena, Nijenhuisa in Wilfa, ki je zanimiva tudi sama po sebi.
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