Intermediate Macdonald Polynomials and Their Vector Versions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908619280220160 |
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| author | Schlösser, Philip |
| author_facet | Schlösser, Philip |
| contents | Intermediate Macdonald polynomials for an affine root system $S$ with fixed origin and finite Weyl group $W_0$ are orthogonal polynomials invariant under a parabolic subgroup $W_J\le W_0$. The extreme cases of $W_J=1$ and $W_J=W_0$ correspond to the non-symmetric and symmetric Macdonald polynomials, respectively.
In this paper we use double-affine Hecke algebras to study their basic properties, including that they form an orthogonal basis and that they diagonalise a commutative algebra of difference-reflection operators, and calculate their norms. Finally, we provide two interpretations of intermediate Macdonald polynomials as vector-valued polynomials of which examples can be found in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_17362 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Intermediate Macdonald Polynomials and Their Vector Versions Schlösser, Philip Representation Theory 33D52, 33D80, 20C08 Intermediate Macdonald polynomials for an affine root system $S$ with fixed origin and finite Weyl group $W_0$ are orthogonal polynomials invariant under a parabolic subgroup $W_J\le W_0$. The extreme cases of $W_J=1$ and $W_J=W_0$ correspond to the non-symmetric and symmetric Macdonald polynomials, respectively. In this paper we use double-affine Hecke algebras to study their basic properties, including that they form an orthogonal basis and that they diagonalise a commutative algebra of difference-reflection operators, and calculate their norms. Finally, we provide two interpretations of intermediate Macdonald polynomials as vector-valued polynomials of which examples can be found in the literature. |
| title | Intermediate Macdonald Polynomials and Their Vector Versions |
| topic | Representation Theory 33D52, 33D80, 20C08 |
| url | https://arxiv.org/abs/2310.17362 |