Exts and Vertex Operators

By Erik Carlsson, A. Okounkov. 2008

137 citations recorded by the source corpus.

The direct product of two Hilbert schemes of the same surface has natural K-theory classes given by the alternating Ext groups between the two ideal sheaves in question, twisted by a line bundle. We express the Chern classes of these virtual bundles in terms of Nakajima operators.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1ae5b03b6f69c444279065ed49b3a408dd74e207

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In Geometry and Topology

1. Sergei Gukov
2. Tudor Dimofte
3. Yuji Tachikawa
4. A. Litvinov
5. V. Fateev
6. F. Benini
7. L. Gottsche
8. Lotte Hollands

In Mathematical Physics

1. Sergei Gukov
2. Tudor Dimofte
3. Yuji Tachikawa
4. L. Alday
5. Lotte Hollands
6. L. Gottsche
7. A. Litvinov
8. V. Fateev

Citations in the corpus

• Affine SL(2) Conformal Blocks from 4d Gauge Theories (2010, background): “The authors are greatly indebted to H. Nakajima and A. Okounkov who kindly and painstakingly explained various mathematical concepts to them.”
• Vortex Counting and Lagrangian 3-Manifolds (2010, background): “Instanton partition functions of U (1) gauge theories can be reformulated as correlation functions of a free boson/free fermion theory [25,26,56].”
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters (2015, unknown): “field formula”: (273) Zinst Ar (a,q)= Y 0≤j<i≤r (1−zi/zj) − p+ i p− j ε1ε2 Thus, we have derived the formulas conjectured in the sections C.1 and C.2 of [2]. Our derivation here differs from that in [18]. For r= 1 we get: Zinst A1 =(1−q) (ε+a0−a1)(a2−a1) ε1ε2 10.3.4. ✿✿✿✿✿ The ✿✿✿✿✿✿✿✿ D-type ✿✿✿✿✿”
• On Combinatorial Expansion of the Conformal Blocks Arising from AGT Conjecture (2010, background): “the conjecture which is the main result of our paper. 2We note that this “strange” form of the vertex operator (2.4) was suggested in somewhat different but related context by Carlsson and Okounkov in [9]. 3In the first row in (2.5) we mean that the differential operator acts only on Virasoro part of t”
• Refined curve counting on complex surfaces (2012, background): “We thank Paolo Aluffi, Florian Block, Barbara Fantechi, Ilia Itenberg, Davesh Maulik, Luca Migliorini, Grigory Mikhalkin, Hiraku Nakajima, Andrei Okounkov, Rahul Pandharipande, Sam Payne, Duco van Straten, Richard Thomas, Kota Yoshioka, and Don Zagier for helpful discussions.”