Infinigens, the Pascal Triangle, and the Witt and Virasoro Algebras

Posted on November 29, 2012 by Tom Copeland

Infinitesimal Generators, the Pascal Pyramid, and the Witt and Virasoro Algebras: A short set of notes sketching some relationships among infinitesimal generators represented as differential operators and infinite-dimensional matrices, the Pascal triangle / pyramid, $SL_2$ conformal transformations, the Witt and Virasoro algebras, the Hermite and generalized Laguerre polynomials of order $-1/2$ , the Dedekind eta function, and combinatorics of the underlying integer matrices, inspired by Alexander Givental’s presentation of Virasoro operators in “Gromov-Witten invariants and quantization of quadratic Hamiltonians.” Some potential connections to knots, flows, dynamics, and Poincare-Maass series are also mentioned.