Hypercontractivity in Group von Neumann Algebras

Provides a combinatorial/numerical method to establish new hypercontractivity estimates in group von Neumann algebras. The authors illustrate their method with free groups, triangular groups and finite cyclic groups, for which they obtain optimal time hypercontractive $L_2 \to L_q$ inequalities with respect to the Markov process given by the word length and with $q$ an even integer.