Plane partitions with a “pit”: generating functions and representation theory

• Mikhail Bershtein ^[1] ; Boris Feigin ^[2] ; Grigory Merzon ^[3]
  1. [1] Landau Institute for Theoretical Physics

     Landau Institute for Theoretical Physics

     Rusia

     
  2. [2] Higher School of Economics, National Research University

     Higher School of Economics, National Research University

     Rusia

     
  3. [3] Moscow Center for Continuous Mathematical Education

  Mostrar afiliaciones +
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 1, 2018, págs. 21-62
• Idioma: inglés
• DOI: 10.1007/s00029-018-0389-z
• Enlaces
  • Texto completo (pdf)
• Resumen

  • We study plane partitions satisfying condition an+1,m+1=0 (this condition is called “pit”) and asymptotic conditions along three coordinate axes. We find the formulas for generating function of such plane partitions. Such plane partitions label the basis vectors in certain representations of quantum toroidal gl1 algebra, therefore our formulas can be interpreted as the characters of these representations. The resulting formulas resemble formulas for characters of tensor representations of Lie superalgebra glm|n. We discuss representation theoretic interpretation of our formulas using q-deformed W-algebra glm|n.