TY - JOUR
AU - Heluani, Reimundo
AB - We prove a new quasiparticle sum expression for the character of the Ising model vertex algebra, related to the Jackson–Slater $q$-series identity of Rogers–Ramanujan type and to Nahm sums for the matrix $\left (\begin {smallmatrix}8&3\\3&2 \end {smallmatrix}\right ) $. We find, as consequences, an explicit monomial basis for the Ising model and a description of its singular support. We find that the ideal sheaf of the latter, defining it as a subscheme of the arc space of its associated scheme, is finitely generated as a differential ideal. We prove three new $q$-series identities of the Rogers–Ramanujan–Slater type associated with the three irreducible modules of the Virasoro Lie algebra of central charge $1/2$. We give a combinatorial interpretation to the identity associated with the vacuum module.
TI - The Singular Support of the Ising Model
JO - International Mathematics Research Notices
DO - 10.1093/imrn/rnab328
DA - 2022-05-06
UR - https://www.deepdyve.com/lp/oxford-university-press/the-singular-support-of-the-ising-model-xSEDLbhvCA
SP - 8800
EP - 8831
VL - 2023
IS - 10
DP - DeepDyve
ER -