2020/09/30 by Alexander Alexandrov, A. Alexandrov
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Algebraic structures and combinatorial models #Combinatorics #Geometry #Group (periodic table) #Hierarchy #Homogeneous space #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum mechanics #Rank (graph theory) #Symmetry (geometry) #hep-th #math-ph #math.AG #math.MP #msc:14N10 #msc:14N35 #msc:37K10 #msc:81R10 #msc:81T32 #nlin.SI
paper · pdf · doi:10.4310/cntp.2021.v15.n3.a6
32 pages, published version
openalex created_date 2020/09/08 · openalex publication_date 2021/01/01 · arxiv created 2021/07/16 · arxiv updated 2021/07/19 · openalex updated_date 2026/08/05
In this paper, we investigate a relation between the Givental group of rank one and the Heisenberg-Virasoro symmetry group of the KP hierarchy. We prove, that only a two-parameter family of the Givental operators can be identified with elements of the Heisenberg-Virasoro symmetry group. This family describes triple Hodge integrals satisfying the Calabi-Yau condition. Using the identification of the elements of two groups we prove that the generating function of triple Hodge integrals satisfying the Calabi-Yau condition and its Θ-version are tau-functions of the KP hierarchy. This generalizes the result of Kazarian on KP integrability in the case of linear Hodge integrals.