The cohomology rings of Hilbert schemes via Jack polynomials

Exts and vertex operators

“…It is known, see [13,6] and also e.g. [12], that the classes of fixed points then correspond to properly normalized Jack polynomials.…”

Orbifold Gromov–Witten theory of the symmetric product of 𝒜r

“…By virtual localization, (3)(4)(5)(6)(7)(8)(9)(10)(11)(12) can be expressed as a sum of residue integrals over T -fixed components. By Lemma 3.1, the invariant (3-12) is˛.t 1 C t 2 / for some rational number˛, and it suffices to evaluate (3-12) over all T -fixed components of the elements in the union`i ;j F E…”

“…Here D .r C 1/ 2 t 2 1 , and ".F /'s are as in (3-13), (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) respectively.…”

“…Hilb kC i .A r // are Heisenberg creation operators; see Grojnowski [11], Li, Qin and Wang [12] and Nakajima [16]. The first equality is Proposition 4.1 while the second equality is [15, Proposition 6.6].…”

“…The configurations (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22) and (3- Recall˛ .E Á/ . z ı/ is the component of .E Á/ relative to the fixed-point class z ı (see (1)(2)).…”