3 research outputs found
Infinite-dimensional -adic groups, semigroups of double cosets, and inner functions on Bruhat--Tits builldings
We construct -adic analogs of operator colligations and their
characteristic functions. Consider a -adic group , its subgroup , and the subgroup
embedded to diagonally. We show that double cosets
admit a structure of a semigroup, acts naturally in -fixed vectors
of unitary representations of . For each double coset we assign a
'characteristic function', which sends a certain Bruhat--Tits building to
another building (buildings are finite-dimensional); image of the distinguished
boundary is contained in the distinguished boundary. The latter building admits
a structure of (Nazarov) semigroup, the product in corresponds to a
point-wise product of characteristic functions.Comment: new version of the paper, 47pp, 3 figure