Murnaghan-Nakayama Rules for the Characters of the Wenzl (k,l)-Representations of the Iwahori-Hecke Algebras of type A

On irreducible characters of the Iwahori-Hecke algebra in type $A$

We use vertex operators to compute irreducible characters of the Iwahori-Hecke algebra of type $A$. Two general formulas are given for the irreducible characters in terms of those of the symmetric groups or the Iwahori-Hecke algebras in lower degrees. Explicit formulas are derived for the irreducible characters labeled by hooks and two-row partitions. Using duality, we also formulate a determinant type Murnaghan-Nakayama formula and give another proof of Ram's combinatorial Murnaghan-Nakayama formula. As applications, we study super-characters of the Iwahori-Hecke algebra as well as the bitrac…

偏微分Hecke代数、Schur-Weyl对偶性与Frobenius特征公式

Mirabolic Hecke algebras, Schur-Weyl duality and Frobenius character formulas

本文研究了偏微分Hecke代数的新的呈现方式，建立了其与量子群之间的Schur-Weyl对偶性，并推导出Frobenius特征公式及递归的Murnaghan-Nakayama规则。

mirabolic Hecke代数的量子超Schur–Weyl对偶与特征标公式

Quantum super Schur--Weyl duality and character formulas for mirabolic Hecke algebras

该研究建立了mirabolic Hecke代数的量子超Schur–Weyl对偶，推导了其不可约特征标的相关公式，还构造了超mirabolic RSK双射，并建立了其与q-rook幺半群代数的参数反转同构以转移相关结果。