Классификация эллиптических γ-матриц, уравнений Книжника-Замолодчикова и соответствующих систем типа Калоджеро-Мозера тема диссертации и автореферата по ВАК РФ 01.04.02, кандидат физико-математических наук Смирнов, Андрей Валерьевич

• Смирнов, Андрей Валерьевич
• кандидат физико-математических наук
• 2013

Оглавление диссертации кандидат физико-математических наук Смирнов, Андрей Валерьевич

1 Введение

1.1 Содержание диссертации.

1.2 Результаты выносимые на защиту диссертации.

2 Голоморфные расслоения над римановыми поверхностями

2.1 Глобальное описание голоморфных расслоений.

2.2 Локальное описание голоморфных расслоений и модификаций.

2.3 Модификация расслоений.

2.4 Голоморфные расслоения над эллиптическими кривыми.

3 Обобщённый базис в Алгебрах Ли

3.1 Построение обобщённого базиса.

3.2 Форма Киллинга в СА-базисе.

3.3 Коммутационные соотношения в СА-базисе.

3.4 Построение интегрируемых систем

4 Некоторые свойства полученных г-матриц

4.1 Классическое уравнение Янга-Бакстера.

4.2 Уравнения Книжника-Замолодчикова для С - расслоений над £т\{г1, .,гп}

5 Пример ЭЦЛГ, С) -система корней ^4дг

5.1 Корни и веса.

5.2 Матрицы переклейки.

5.3 Базисы

5.4 Операторы Лакса и Гамильтонианы.

6 Тригонометрический и рациональный пределы

6.1 Основной пример: Ранг 2.

6.2 Формулы для случая произвольного ранга.

6.3 Квантовые Д-матрицы

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