The Murnaghan―Nakayama rule for k-Schur functions

• الحاوية / القاعدة: Discrete Mathematics & Theoretical Computer Science
• المؤلفون الرئيسيون: Jason Bandlow, Anne Schilling, Mike Zabrocki
• التنسيق: مقال
• اللغة: الإنجليزية
• منشور في: Discrete Mathematics & Theoretical Computer Science 2011-01-01
• الموضوعات: murnaghan―nayakama rule; symmetric functions; noncommutative symmetric functions; k-schur functions; [math.math-co] mathematics [math]/combinatorics [math.co]; [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
• الوصول للمادة أونلاين: https://dmtcs.episciences.org/2894/pdf
• تدمد: 1365-8050

We prove a Murnaghan–Nakayama rule for k-Schur functions of Lapointe and Morse. That is, we give an explicit formula for the expansion of the product of a power sum symmetric function and a k-Schur function in terms of k-Schur functions. This is proved using the noncommutative k-Schur functions in terms of the nilCoxeter algebra introduced by Lam and the affine analogue of noncommutative symmetric functions of Fomin and Greene.