{
  "id": "2404.10266",
  "version": "v1",
  "published": "2024-04-16T03:37:25.000Z",
  "updated": "2024-04-16T03:37:25.000Z",
  "title": "Irreducible components in Hochschild cohomology of flag varieties",
  "authors": [
    "Sam Jeralds"
  ],
  "comment": "12 pages",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "Let $G$ be a simple, simply-connected complex algebraic group with Lie algebra $\\mathfrak{g}$, and $G/B$ the associated complete flag variety. The Hochschild cohomology $HH^\\bullet(G/B)$ is a geometric invariant of the flag variety related to its generalized deformation theory and has the structure of a $\\mathfrak{g}$-module. We study this invariant via representation-theoretic methods; in particular, we give a complete list of irreducible subrepresentations in $HH^\\bullet(G/B)$ when $G=SL_n(\\mathbb{C})$ or is of exceptional type (and conjecturally for all types) along with nontrivial lower bounds on their multiplicities. These results follow from a conjecture due to Kostant on the structure of the tensor product representation $V(\\rho) \\otimes V(\\rho)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-16T03:37:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M15",
      "17B10",
      "14F43"
    ],
    "keywords": [
      "hochschild cohomology",
      "irreducible components",
      "nontrivial lower bounds",
      "associated complete flag variety",
      "tensor product representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}