Functorial transfer of Cohomological Representations from $SP(4,\mathbb{R})$ to $GL(5,\mathbb{R})$

Makarand Sarnobat

Functorial transfer of Cohomological Representations from $SP(4,\mathbb{R})$ to $GL(5,\mathbb{R})$

Number Theory 2019-11-05 v2 Representation Theory

Authors: Makarand Sarnobat

Abstract

Let $G=Sp(4,\mathbb{R})$ and let $\pi$ be an irreducible, unitary representation of $G$ which is cohomological with respect to trivial coefficients. Using the inclusion from $SO(5,\mathbb{C})$ to $GL(5,\mathbb{C})$ , we transfer $\pi$ to an irreducible representation $\iota(\pi)$ of $GL(5,\mathbb{R})$ and determine how the property of being cohomological behaves under Langlands functoriality. We also consider representations which are cohomological with respect to non-trivial coefficients.

Keywords

cohomological representations langlands functoriality sp(4,r) gl(5,r) unitary representations trivial coefficients

Cite

@article{arxiv.1905.03940,
  title  = {Functorial transfer of Cohomological Representations from $SP(4,\mathbb{R})$ to $GL(5,\mathbb{R})$},
  author = {Makarand Sarnobat},
  journal= {arXiv preprint arXiv:1905.03940},
  year   = {2019}
}

Functorial transfer of Cohomological Representations from $SP(4,\mathbb{R})$ to $GL(5,\mathbb{R})$

Abstract

Keywords

Cite

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