The volumes of Miyauchi subgroups

Area of Science:

• Number Theory
• Representation Theory
• Algebraic Groups

Background:

• Miyauchi introduced L and factors for generic representations of the unramified unitary group of rank three.
• These factors are defined using local newforms and sequences of subgroups.

Purpose of the Study:

• To compute the volumes of the Miyauchi groups associated with these representations.

Main Methods:

• The study involves calculations based on the definitions provided by Miyauchi.
• Utilizes concepts of local newforms and subgroup structures.

Main Results:

• The volumes of the specific Miyauchi groups have been successfully calculated.
• Provides concrete values for these geometric objects in representation theory.

Conclusions:

• The calculation of Miyauchi group volumes offers insights into the structure of automorphic representations.
• This work contributes to the understanding of the unramified unitary group of rank three.