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Formulas for Koornwinder polynomials — arXiv:2608.02810

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.02810
License (as archived): CC0-1.0
Archived: 2026-10-31T12:55:44.897Z
SHA-256 of the archived text: a5913f092441242d0350b1bcdd335f319ba8751d58748e75f511f517340f186f
Stable URL of this page: https://metraipolis.com/documento/dc_ae47003cd34c

How to cite

Formulas for Koornwinder polynomials — arXiv:2608.02810 — arXiv (en), https://arxiv.org/abs/2608.02810 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ae47003cd34c (Metraipolis archive dc_ae47003cd34c, sha256 a5913f092441242d0350b1bcdd335f319ba8751d58748e75f511f517340f186f)

BibTeX

@misc{dcae47003cd34c,
  title = {Formulas for Koornwinder polynomials — arXiv:2608.02810},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.02810},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ae47003cd34c; sha256 a5913f092441242d0350b1bcdd335f319ba8751d58748e75f511f517340f186f},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.02810. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This paper provides formulas for Koornwinder polynomials in analogy with the creation formula, the alcove walk formula and the non-attacking fillings formula for the type $GL_n$ Macdonald polynomials. We state the creation formula in terms of the divided-difference operators used in Schubert calculus, and we use a box-greedy reduced word to reformulate the alcove walk formula in terms of uncompressed set-valued tableaux. Then two types of compression, ``around-the-end compression'' and ``across-the-$0$-gap compression'', are used to derive a formula for Koornwinder polynomials in terms of compressed set-valued tableaux. Throughout we work in the full generality of relative Koornwinder polynomials, which are the analogues of the permuted basement Macdonald polynomials used in the type $GL_n$ case.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-05 in math.CO).
Categorie arXiv: Combinatorics (math.CO) ; Representation Theory (math.RT).
Pagina del lavoro: https://arxiv.org/abs/2608.02810 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-31T12:42:47.751Z dalla pagina https://arxiv.org/catchup/math.CO/2026-08-05?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).