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A new approach to the representation theory of the symmetric groups, III: Induced representations and the Frobenius--Young correspondence

机译：对称群表示理论的一种新方法， III：诱导表征和Frobenius - Young对应

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We give a new (inductive) proof of the classical Frobenius--Youngcorrespondence between irreducible complex representations of the symmetricgroup and Young diagrams, using the new approach, suggested in \cite{OV, VO},to determining this correspondence. We also give linear relations betweenKostka numbers that follow from the decomposition of the restrictions ofinduced representations to the previous symmetric subgroup. We consider arealization of representations induced from Young subgroups in polylinear formsand describe its relation to Specht modules.

机译：我们使用\ cite {OV，VO}中建议的新方法，确定对称性，给出了经典Frobenius--对称组的不可约复杂表示与Young图之间的年轻对应的新（归纳）证明。我们还给出了Kostka数之间的线性关系，这些关系是从归纳表示的限制分解到先前的对称子组之后得出的。我们考虑了由多线性形式的Young子组引起的表示的区域化，并描述了其与Specht模块的关系。

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Vershik, A.;
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年度 2006
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1. A New Approach to the Representation Theory of the Symmetric Groups, III: Induced Representations and the Frobenius–Young Correspondence [J] . A. Vershik Moscow mathematical journal . 2006,第3期

机译：对称群表示理论的一种新方法，III：归纳表示与弗罗宾纽斯·杨对应
2. A NEW APPROACH TO THE REPRESENTATION THEORY OF THE SYMMETRIC GROUPS, IV. Z(2)-GRADED GROUPS AND ALGEBRAS; PROJECTIVE REPRESENTATIONS OF THE GROUP S-n [J] . Vershik AM, Sergeev AN Moscow mathematical journal . 2008,第4期

机译：对称群表示理论的一种新方法，IV。 Z（2）级组和代数; S-n组的投射表示
3. A NEW APPROACH TO THE REPRESENTATION THEORY OF THE SYMMETRIC GROUPS. IV. Z(2)-GRADED GROUPS AND ALGEBRAS (vol 8, pg 813, 2008) [J] . Vershik A., Sergeev A. Moscow mathematical journal . 2018,第1期

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4. Representation theory of the symmetric group in voting theory and game theory [C] . Karl-Dieter Crisman, Michael E. Orrison AMS Special Session on Algebraic and Geometric Methods in Applied Discrete Mathematics . 2017

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5. A correspondence theory of musical representation [D] . Polite, Brandon E. 2010

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6. On the Modular Representations of the Symmetric Group (III) [O] . G. de B. Robinson 1952

机译：关于对称群（III）的模块化表示
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Gustav and KnightS. (eds), British Industrial Fictions , University of Wales Press, 2000, pp. viii + 212, £14.99 pb.; BalchJack S., Lamps at High Noon , University of Illinois Press, 2000, pp. xl + 404, $19.45 pb.; ConroyJack, A World to Win , University of Illinois Press, 2000, pp. xxxv + 348, $17.95 pb.GagnierRegenia, The Insatiability of Human Wants: Economics and Aesthetics in Market Society , University of Chicago Press, 2000, pp. 352, £10.50 pb. [O] . Paul Hyland, R. C. Richardson, Ivan Roots, 2001

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A new approach to the representation theory of the symmetric groups, III: Induced representations and the Frobenius--Young correspondence

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