{
  "id": "2506.17907",
  "version": "v1",
  "published": "2025-06-22T06:01:41.000Z",
  "updated": "2025-06-22T06:01:41.000Z",
  "title": "The endoscopic character identity for even special orthogonal groups",
  "authors": [
    "Hao Peng"
  ],
  "comment": "17 pages, comments welcome!",
  "categories": [
    "math.RT"
  ],
  "abstract": "We establish the endoscopic character identity for bounded $A$-packets of non-quasi-split even special orthogonal groups, with respect to elliptic endoscopic triples. The proof reduces the non-quasi-split case to the quasi-split case and the real Adam--Johnson case by combining local-global compatibility principle with Arthur's multiplicity formula for non-quasi-split even special orthogonal groups established by Chen and Zou in arXiv:2103.07956. This result plays a key role in the author's work arXiv:2503.04623 on the compatibility between the Fargues--Scholze local Langlands correspondence and classical local Langlands correspondence for even special orthogonal groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-06-22T06:01:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "special orthogonal groups",
      "endoscopic character identity",
      "fargues-scholze local langlands correspondence",
      "classical local langlands correspondence",
      "elliptic endoscopic triples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}