TY - JOUR
T1 - Highest-Weight Vectors and Three-Point Functions in GKO Coset Decomposition
AU - Bershtein, Mikhail
AU - Feigin, Boris
AU - Trufanov, Aleksandr
N1 - Publisher Copyright:
© Crown 2025.
PY - 2025/6
Y1 - 2025/6
N2 - We revisit the classical Goddard–Kent–Olive coset construction. We find the formulas for the highest weight vectors in coset decomposition and calculate their norms. We also derive formulas for matrix elements of natural vertex operators between these vectors. This leads to relations on conformal blocks. Due to the AGT correspondence, these relations are equivalent to blowup relations on Nekrasov partition functions with the presence of the surface defect. These relations can be used to prove Kyiv formulas for the Painlevé tau-functions (following Nekrasov’s method).
AB - We revisit the classical Goddard–Kent–Olive coset construction. We find the formulas for the highest weight vectors in coset decomposition and calculate their norms. We also derive formulas for matrix elements of natural vertex operators between these vectors. This leads to relations on conformal blocks. Due to the AGT correspondence, these relations are equivalent to blowup relations on Nekrasov partition functions with the presence of the surface defect. These relations can be used to prove Kyiv formulas for the Painlevé tau-functions (following Nekrasov’s method).
UR - http://www.scopus.com/inward/record.url?scp=105006680171&partnerID=8YFLogxK
U2 - 10.1007/s00220-025-05318-1
DO - 10.1007/s00220-025-05318-1
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
C2 - 40443483
AN - SCOPUS:105006680171
SN - 0010-3616
VL - 406
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 6
M1 - 142
ER -