scholarly journals Zeta-functions of root systems and Poincaré polynomials of Weyl groups

2020 ◽  
Vol 72 (1) ◽  
pp. 87-126
Author(s):  
Yasushi Komori ◽  
Kohji Matsumoto ◽  
Hirofumi Tsumura
Keyword(s):  
Zeta Functions ◽  
Root Systems ◽  
Weyl Groups

scholarly journals Zeta Functions of Root Systems

2006 ◽  
pp. 115-140 ◽  
Author(s):  
Y. KOMORI ◽  
K. MATSUMOTO ◽  
H. TSUMURA
Keyword(s):  
Zeta Functions ◽  
Root Systems

INVERSIONS IN CLASSICAL WEYL GROUPS

2007 ◽  
Vol 09 (01) ◽  
pp. 1-20
Author(s):  
KEQUAN DING ◽  
SIYE WU
Keyword(s):  
Finite Group ◽  
Weyl Group ◽  
Root Systems ◽  
Flag Manifold ◽  
Length Function ◽  
Weyl Groups ◽  
Flag Manifolds ◽  
A Finite Group

We introduce inversions for classical Weyl group elements and relate them, by counting, to the length function, root systems and Schubert cells in flag manifolds. Special inversions are those that only change signs in the Weyl groups of types Bn, Cnand Dn. Their counting is related to the (only) generator of the Weyl group that changes signs, to the corresponding roots, and to a special subvariety in the flag manifold fixed by a finite group.

FUNCTIONAL RELATIONS FOR ZETA-FUNCTIONS OF ROOT SYSTEMS

Number Theory ◽  
2009 ◽  
Author(s):  
YASUSHI KOMORI ◽  
KOHJI MATSUMOTO ◽  
HIROFUMI TSUMURA
Keyword(s):  
Zeta Functions ◽  
Root Systems ◽  
Functional Relations

scholarly journals The Garnir Relations for Weyl Groups of Type $C_n$

10.37236/797 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Himmet Can
Keyword(s):  
Symmetric Groups ◽  
Root Systems ◽  
Weyl Groups ◽  
Specht Modules ◽  
Combinatorial Description ◽  
Combinatorial Constructions

The Garnir relations play a very important role in giving combinatorial constructions of representations of the symmetric groups. For the Weyl groups of type $C_n$, having obtained the alternacy relation, we give an explicit combinatorial description of the Garnir relation associated with a $\Delta$-tableau in terms of root systems. We then use these relations to find a $K$-basis for the Specht modules of the Weyl groups of type $C_n$.

scholarly journals Multiple zeta values and zeta-functions of root systems

2011 ◽  
Vol 87 (6) ◽  
pp. 103-107 ◽  
Author(s):  
Yasushi Komori ◽  
Kohji Matsumoto ◽  
Hirofumi Tsumura
Keyword(s):  
Zeta Functions ◽  
Root Systems ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values

scholarly journals Submodules of Specht modules for Weyl groups

1996 ◽  
Vol 39 (1) ◽  
pp. 43-50
Author(s):  
Saіt Halicioğlu
Keyword(s):  
Characteristic Zero ◽  
Symmetric Groups ◽  
Root Systems ◽  
Weyl Groups ◽  
Arbitrary Field ◽  
Specht Modules ◽  
Irreducible Modules

The construction of all irreducible modules of the symmetric groups over an arbitrary field which reduce to Specht modules in the case of fields of characteristic zero is given by G. D. James. Halicioğlu and Morris describe a possible extension of James' work for Weyl groups in general, where Young tableux are interpreted in terms of root systems. In this paper we show how to construct submodules of Specht modules for Weyl groups.

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