{
  "id": "1502.05322",
  "version": "v1",
  "published": "2015-02-18T17:56:37.000Z",
  "updated": "2015-02-18T17:56:37.000Z",
  "title": "Demazure Flags, Chebyshev polynomials, Partial and Mock theta functions",
  "authors": [
    "Rekha Biswal",
    "Vyjayanthi Chari",
    "Lisa Schneider",
    "Sankaran Viswanath"
  ],
  "comment": "31 pages",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We study the level $m$--Demazure flag of a level $\\ell$--Demazure module for $\\frak{sl}_2[t]$. We define the generating series $A_n^{\\ell \\rightarrow m}(x,q)$ which encodes the $q$--multiplicity of the level $m$ Demazure module of weight $n$. We establish two recursive formulae for these functions. We show that the specialization to $q=1$ is a rational function involving the Chebyshev polynomials. We give a closed form for $A_n^{\\ell \\rightarrow \\ell+1}(x,q)$ and prove that it is given by a rational function. In the case when $m=\\ell+1$ and $\\ell=1,2$, we relate the generating series to partial theta series. We also study the specializations $A_n^{1\\rightarrow 3}(q^k,q)$ and relate them to the fifth order mock-theta functions of Ramanujan.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-18T17:56:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mock theta functions",
      "demazure flag",
      "chebyshev polynomials",
      "fifth order mock-theta functions",
      "rational function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}