Measure and integration on \(\mathrm{GL}_2\) over a two-dimensional local field (Q2329058)

Based on authors' abstract: The author defines a translation-invariant measure and integral on GL\(_2\) over a two-dimensional local field \(F\) by combining elements of the classical GL\(_2\) theory and the theory developed by \textit{I. Fesenko} [Doc. Math. Extra Vol., Kazuya Kato's Fiftieth Birthday, 261--284 (2003; Zbl 1130.11335)] for the field \(F\) itself. Several expressions for the integral are given, including one which agrees with the integral defined previously by \textit{M. Morrow} [Commun. Number Theory Phys. 2, No. 3, 563--592 (2008; Zbl 1171.28303)].