Trace formula for finite groups and the Macdonald correspondence for GL(F)

Kazım İlhan İkeda

Makale detayları

Trace formula for finite groups and the Macdonald correspondence for GL(F)

Yazarlar:

Kazım İlhan İkeda

Yayıncı:

Istanbul University

Ana Başlıklar:

Pure Mathematics (Other)

Dergi:

Istanbul Journal of Mathematics Vol.2 Issue 2, pp.55-69

Belge Tipi:

Makale

Yayın Tarihi:

12/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001340649

pISSN:

2980-3020

Anahtar kelimeler:

Özet:

 Let  be a finite group. The trace formula for , which is the trivial case of the Arthur trace formula, is well known with many applications. In this note, we further consider a subgroup Γ of  and a representation  : Γ  GL of Γ on a finite dimensional C-vector space, and compute the trace TrInd Γ     of the operator Ind Γ    : Ind Γ   Ind Γ  for any function  :   C in two different ways. The expressions for TrInd Γ     denoted by  ,   and ,   are the spectral side and the geometric side of the trace formula for TrInd Γ    , respectively. The identity  ,    TrInd Γ      ,   is a generalization of the trace formula for the finite group . This theory is then applied to the automorphic side of the Macdonald correspondence for GL F; namely, to the automorphic side of the local 0-dimensional Langlands correspondence for GL, where new identities are obtained for the -factors of representations of GL F.

 Let  be a finite group. The trace formula for , which is the trivial case of the Arthur trace formula, is well known with many applications. In this note, we further consider a subgroup Γ of  and a representation  : Γ  GL of Γ on a finite dimensional C-vector space, and compute the trace TrInd Γ     of the operator Ind Γ    : Ind Γ   Ind Γ  for any function  :   C in two different ways. The expressions for TrInd Γ     denoted by  ,   and ,   are the spectral side and the geometric side of the trace formula for TrInd Γ    , respectively. The identity  ,    TrInd Γ      ,   is a generalization of the trace formula for the finite group . This theory is then applied to the automorphic side of the Macdonald correspondence for GL F; namely, to the automorphic side of the local 0-dimensional Langlands correspondence for GL, where new identities are obtained for the -factors of representations of GL F.

 Let  be a finite group. The trace formula for , which is the trivial case of the Arthur trace formula, is well known with many applications. In this note, we further consider a subgroup Γ of  and a representation  : Γ  GL of Γ on a finite dimensional C-vector space, and compute the trace TrInd Γ     of the operator Ind Γ    : Ind Γ   Ind Γ  for any function  :   C in two different ways. The expressions for TrInd Γ     denoted by  ,   and ,   are the spectral side and the geometric side of the trace formula for TrInd Γ    , respectively. The identity  ,    TrInd Γ      ,   is a generalization of the trace formula for the finite group . This theory is then applied to the automorphic side of the Macdonald correspondence for GL F; namely, to the automorphic side of the local 0-dimensional Langlands correspondence for GL, where new identities are obtained for the -factors of representations of GL F.

 Let  be a finite group. The trace formula for , which is the trivial case of the Arthur trace formula, is well known with many applications. In this note, we further consider a subgroup Γ of  and a representation  : Γ  GL of Γ on a finite dimensional C-vector space, and compute the trace TrInd Γ     of the operator Ind Γ    : Ind Γ   Ind Γ  for any function  :   C in two different ways. The expressions for TrInd Γ     denoted by  ,   and ,   are the spectral side and the geometric side of the trace formula for TrInd Γ    , respectively. The identity  ,    TrInd Γ      ,   is a generalization of the trace formula for the finite group . This theory is then applied to the automorphic side of the Macdonald correspondence for GL F; namely, to the automorphic side of the local 0-dimensional Langlands correspondence for GL, where new identities are obtained for the -factors of representations of GL F.

Makale detayları

Trace formula for finite groups and the Macdonald correspondence for GL(F)

Yazarlar: Kazım İlhan İkeda

Yayıncı: Istanbul University

Ana Başlıklar: Pure Mathematics (Other)

Dergi: Istanbul Journal of Mathematics Vol.2 Issue 2, pp.55-69

Belge Tipi: Makale

Yayın Tarihi: 12/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001340649

pISSN: 2980-3020

Trace formula

finite group

Macdonald correspondence

Sayı

Yazarlar:

Kazım İlhan İkeda

Yayıncı:

Istanbul University

Ana Başlıklar:

Pure Mathematics (Other)

Dergi:

Istanbul Journal of Mathematics Vol.2 Issue 2, pp.55-69

Belge Tipi:

Makale

Yayın Tarihi:

12/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001340649

pISSN:

2980-3020