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Langlands Duality and Invariant Differential Operators: the Case SL(2n+1)

  • V. K. Dobrev
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Abstract

Recently we started building a bridge between two cases of Langlands duality. The latter is one of the most influential topics in mathematical research. It has many different appearances and influential subtopics. Yet there is a topic that until now seems unrelated to the Langlands program. That is the topic of invariant differential operators. That is strange since both items are deeply rooted in Harish-Chandra's representation theory of semisimple Lie groups. We started with the case of the group ~SL(2n). In the present paper we deal with the group SL(2n+1). The two mentioned groups are similar, but their representation theories is rather different.

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Cite

BibTeXRIS
BibTeX
@misc{dobrev2026langlands,
  title = {{Langlands Duality and Invariant Differential Operators: the Case SL(2n+1)}},
  author = {V. K. Dobrev},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.13400},
  eprint = {2608.13400},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.13400},
}
RIS
TY  - UNPB
TI  - Langlands Duality and Invariant Differential Operators: the Case SL(2n+1)
AU  - V. K. Dobrev
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2608.13400
UR  - https://arxiv.org/abs/2608.13400
AB  - Recently we started building a bridge between two cases of Langlands duality. The latter is one of the most influential topics in mathematical research. It has many different appearances and influential subtopics. Yet there is a topic that until now seems unrelated to the Langlands program. That is the topic of invariant differential operators. That is strange since both items are deeply rooted in Harish-Chandra's representation theory of semisimple Lie groups. We started with the case of the group ~SL(2n). In the present paper we deal with the group SL(2n+1). The two mentioned groups are similar, but their representation theories is rather different.
ER  -