اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA new tableau model for irreducible polynomial representations of the orthogonal group
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تأليف
Hideya Watanabe
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We provide a new tableau model from which one can easily deduce the characters of irreducible polynomial representations of the orthogonal group $mathrm{O}_n(mathbb{C})$. This model originates from representation theory of the $imath$quantum group of type AI, and is equipped with a combinatorial structure, which we call AI-crystal structure. This structure enables us to describe combinatorially the tensor product of an $mathrm{O}_n(mathbb{C})$-module and a $mathrm{GL}_n(mathbb{C})$-module, and the branching from $mathrm{GL}_n(mathbb{C})$ to $mathrm{O}_n(mathbb{C})$.
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