# Miura opers and critical points of master functions

Evgeny Mukhin; Alexander Varchenko

Open Mathematics (2005)

- Volume: 3, Issue: 2, page 155-182
- ISSN: 2391-5455

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topEvgeny Mukhin, and Alexander Varchenko. "Miura opers and critical points of master functions." Open Mathematics 3.2 (2005): 155-182. <http://eudml.org/doc/268827>.

@article{EvgenyMukhin2005,

abstract = {Critical points of a master function associated to a simple Lie algebra \[\mathfrak \{g\}\]
come in families called the populations [11]. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra \[^t \mathfrak \{g\}\]
. The proof is based on the correspondence between critical points and differential operators called the Miura opers. For a Miura oper D, associated with a critical point of a population, we show that all solutions of the differential equation DY=0 can be written explicitly in terms of critical points composing the population.},

author = {Evgeny Mukhin, Alexander Varchenko},

journal = {Open Mathematics},

keywords = {82B23; 17B67; 14M15},

language = {eng},

number = {2},

pages = {155-182},

title = {Miura opers and critical points of master functions},

url = {http://eudml.org/doc/268827},

volume = {3},

year = {2005},

}

TY - JOUR

AU - Evgeny Mukhin

AU - Alexander Varchenko

TI - Miura opers and critical points of master functions

JO - Open Mathematics

PY - 2005

VL - 3

IS - 2

SP - 155

EP - 182

AB - Critical points of a master function associated to a simple Lie algebra \[\mathfrak {g}\]
come in families called the populations [11]. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra \[^t \mathfrak {g}\]
. The proof is based on the correspondence between critical points and differential operators called the Miura opers. For a Miura oper D, associated with a critical point of a population, we show that all solutions of the differential equation DY=0 can be written explicitly in terms of critical points composing the population.

LA - eng

KW - 82B23; 17B67; 14M15

UR - http://eudml.org/doc/268827

ER -

## References

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