论文标题
i-Quantum group u^J（n）的新实现
A new realization of the i-quantum group U^j(n)
论文作者
论文摘要
我们遵循Beilinson-Lusztig-Macpherson开发的方法，并由FU和第一作者进行了修改，以研究B型i- Quantum组U^J（n）的新实现，并在[BKLW，Lem。〜3.2]中发现的乘法公式建立在乘积公式上。这使我们能够通过生成器通过基础和乘法公式呈现u^j（n）。我们还建立了从u^j（n）的lusztig类型形式到B型的Q-Schur代数的分支代数同构。因此，基本变化使我们能够将U^J（n）的i- Quantum hyperalgebras的表示形式联系起来，u^j（n）的I- Quantum Hyperalgebras在未定义的奇数奇数中的有限正交群体的代表。这将Dipper的一部分概括为B型情况。
We follow the approach developed by Beilinson-Lusztig-MacPherson and modified by Fu and the first author to investigate a new realization for the i-quantum groups U^j(n) of type B, building on the multiplication formulas discovered in [BKLW,Lem.~3.2]. This allows us to present U^j(n) via a basis and multiplication formulas by generators. We also establish a surjective algebra homomorphism from a Lusztig type form of U^j(n) to integral q-Schur algebras of type B. Thus, base changes allow us to relate representations of the i-quantum hyperalgebras of U^j(n) to representations of finite orthogonal groups of odd degree in non-defining characteristics. This generalizes part of Dipper--James' type A theory to the type B case.
