dorsal/arxiv
View SchemaA $q$-analogue of the type $A$ Dunkl operator and integral kernel
| Authors | T. H. Baker, P. J. Forrester |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9701039 |
| URL | https://arxiv.org/abs/q-alg/9701039 |
Abstract
We introduce the $q$-analogue of the type $A$ Dunkl operators, which are a set of degree--lowering operators on the space of polynomials in $n$ variables. This allows the construction of raising/lowering operators with a simple action on non-symmetric Macdonald polynomials. A bilinear series of non-symmetric Macdonald polynomials is introduced as a $q$-analogue of the type $A$ Dunkl integral kernel ${\cal K}_A(x;y)$. The aforementioned operators are used to show that the function satisfies $q$-analogues of the fundamental properties of ${\cal K}_A(x;y)$.
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"abstract": "We introduce the $q$-analogue of the type $A$ Dunkl operators, which are a\nset of degree--lowering operators on the space of polynomials in $n$ variables.\nThis allows the construction of raising/lowering operators with a simple action\non non-symmetric Macdonald polynomials. A bilinear series of non-symmetric\nMacdonald polynomials is introduced as a $q$-analogue of the type $A$ Dunkl\nintegral kernel ${\\cal K}_A(x;y)$. The aforementioned operators are used to\nshow that the function satisfies $q$-analogues of the fundamental properties of\n${\\cal K}_A(x;y)$.",
"arxiv_id": "q-alg/9701039",
"authors": [
"T. H. Baker",
"P. J. Forrester"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "A $q$-analogue of the type $A$ Dunkl operator and integral kernel",
"url": "https://arxiv.org/abs/q-alg/9701039"
},
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