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Colored vertex models and Iwahori Whittaker functions
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- Brubaker, Ben (författare)
- University of Minnesota,School of Mathematics, University of Minnesota, MN, Minneapolis, United States
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- Buciumas, Valentin (författare)
- Pohang University of Science and Technology,Department of Mathematics, Pohang University of Science and Technology, Pohang, South Korea
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- Bump, Daniel (författare)
- Stanford University,Department of Mathematics, Stanford University, CA, Stanford, United States
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- Gustafsson, Henrik, 1988 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Umeå universitet,Umeå University,Chalmers tekniska högskola,Chalmers University of Technology,Rutgers University,Stanford University,Institutionen för matematik och matematisk statistik,Department of Mathematics, Stanford University, CA, Stanford, United States; School of Mathematics, Institute for Advanced Study, NJ, Princeton, United States; Department of Mathematics, Rutgers University, NJ, Piscataway, United States; Department of Mathematical Sciences, University of Gothenburg and Chalmers University of Technology, Gothenburg, Sweden
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(creator_code:org_t)
- Springer Nature, 2024
- 2024
- Engelska.
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Ingår i: Selecta Mathematica, New Series. - : Springer Nature. - 1420-9020 .- 1022-1824. ; 30:4
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Abstract
Ämnesord
Stäng
- We give a recursive method for computing all values of a basis of Whittaker functions for unramified principal series invariant under an Iwahori or parahoric subgroup of a split reductive group G over a nonarchimedean local field F. Structures in the proof have surprising analogies to features of certain solvable lattice models. In the case G=GLr we show that there exist solvable lattice models whose partition functions give precisely all of these values. Here ‘solvable’ means that the models have a family of Yang–Baxter equations which imply, among other things, that their partition functions satisfy the same recursions as those for Iwahori or parahoric Whittaker functions. The R-matrices for these Yang–Baxter equations come from a Drinfeld twist of the quantum group Uq(gl^(r|1)), which we then connect to the standard intertwining operators on the unramified principal series. We use our results to connect Iwahori and parahoric Whittaker functions to variations of Macdonald polynomials.
Ämnesord
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
- NATURVETENSKAP -- Matematik -- Geometri (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Geometry (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Diskret matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Discrete Mathematics (hsv//eng)
Nyckelord
- 16T25
- Quantum group
- 05E05
- Primary 22E50
- Parahoric Whittaker function
- Demazure operator
- 82B23
- Yang–Baxter equation
- Macdonald polynomial
- Whittaker function
- Secondary 11F70
- Iwahori Whittaker function
- Solvable lattice model
- Whittaker function
- Iwahori Whittaker function
- Parahoric Whittaker function
- Demazure operator
- Macdonald polynomial
- Solvable lattice model
- Yang-Baxter equation
- Quantum group
Publikations- och innehållstyp
- art (ämneskategori)
- ref (ämneskategori)
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