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Ward identities and W-constraints in Generalized Kontsevich Model

The connection is obtained between Ward identities and W-constraints in Generalized Kontsevich Model with the potential $X^4/4$. We show that Ward identities include W-constraints (and do not include any other constraints) for this potential and make some observations in favour of the same connection for the model with the potential of the form $X^{(K+1)}/(K+1)$ for any $K\geq 2$.