TY  - JOUR
ID  - Cho2016
LB  - Cho2016
AU  - Cho, Ilwoo
TI  - Certain group dynamical systems induced by Hecke algebras
ST  - Certain group dynamical systems induced by Hecke algebras
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2016
VL  - 36
IS  - 3
SP  - 337
EP  - 373
DO  - http://dx.doi.org/10.7494/OpMath.2016.36.3.337
UR  - http://dx.doi.org/10.7494/OpMath.2016.36.3.337
AB  - In this paper, we study dynamical systems induced by a certain group \(\mathfrak{T}_{N}^{K}\) embedded in the Hecke algebra \(\mathcal{H}(G_{p})\) induced by the generalized linear group \(G_{p} = GL_{2}(\mathbb{Q}_{p})\) over the \(p\)-adic number fields \(\mathbb{Q}_{p}\) for a fixed prime \(p\). We study fundamental properties of such dynamical systems and the corresponding crossed product algebras in terms of free probability on the Hecke algebra \(\mathcal{H}(G_{p})\).
KW  - free probability
KW  - free moments
KW  - free cumulants
KW  - Hecke algebra
KW  - normal Hecke subalgebra
KW  - free probability spaces
KW  - representations
KW  - operators
KW  - Hilbert spaces
KW  - dynamical systems
KW  - crossed product algebras
SN  - 1232-9274
ER  -