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Non-Abelian W-representation for GKM

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arxiv 2107.02210 v1 pith:6RT3SCCA submitted 2021-07-05 hep-th math-phmath.MP

Non-Abelian W-representation for GKM

classification hep-th math-phmath.MP
keywords operatorsmatrixmodelsactionappearanceconstraintsdefinedifferent
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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abstract

$W$-representation is a miraculous possibility to define a non-perturbative (exact) partition function as an exponential action of somehow integrated Ward identities on unity. It is well known for numerous eigenvalue matrix models when the relevant operators are of a kind of $W$-operators: for the Hermitian matrix model with the Virasoro constraints, it is a $W_3$-like operator, and so on. We extend this statement to the monomial generalized Kontsevich models (GKM), where the new feature is the appearance of an ordered P-exponential for the set of non-commuting operators of different gradings.

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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.