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arxiv 1009.4887 v3 pith:MBHJCP3P submitted 2010-09-24 hep-th math-phmath.COmath.MP

Cut-and-Join operator representation for Kontsevich-Witten tau-function

classification hep-th math-phmath.COmath.MP
keywords cut-and-joinkontsevich-wittenoperatorrepresentationtau-functionapplicationsconstraintsconstruct
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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In this short note we construct a simple cut-and-join operator representation for Kontsevich-Witten tau-function that is the partition function of the two-dimensional topological gravity. Our derivation is based on the Virasoro constraints. Possible applications of the obtained expression are discussed.

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    Proves uniqueness of solutions to constraints on (q,t)-deformed hypergeometric functions and derives superintegrability relations for a general (q,t)-deformed matrix model with allowed parameters.