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Jucys-Murphy elements of partition algebras for the rook monoid [article]

Ashish Mishra, Shraddha Srivastava
2020 arXiv   pre-print
This paper studies the representation theory of partition algebras CI_k and CI_k+1/2 for rook monoids inductively by considering the multiplicity free tower C I_1⊂C I_3/2⊂C I_2⊂...  ...  Kudryavtseva and Mazorchuk exhibited Schur-Weyl duality between the rook monoid algebra CR_n and the subalgebra CI_k of the partition algebra C A_k(n) acting on (C^n)^⊗ k.  ...  James East for pointing out the paper [5] which studies the cellularity of totally propapgating partition algebras. S.S. thanks Prof.  ... 
arXiv:1912.10737v3 fatcat:hgg5gdhihbevdnju625xbe4koy

Jucys-Murphy elements and Grothendieck groups for generalized rook monoids [article]

Volodymyr Mazorchuk, Shraddha Srivastava
2021 arXiv   pre-print
We construct simple modules and describe Jucys-Murphy elements for generalized rook monoid algebras.  ...  Over an algebraically closed field of positive characteristic p, utilizing Jucys-Murphy elements of rook monoid algebras, for 0≤ i≤ p-1 we define the corresponding i-restriction and i-induction functors  ...  The case of rook monoids. Recall Jucys-Murphy elements of Z[R n ]: g r := i1,...  ... 
arXiv:2104.13632v2 fatcat:ajrhxkfa3bhcbdnebva7r25xse

Presentations for rook partition monoids and algebras and their singular ideals [article]

James East
2016 arXiv   pre-print
We obtain several presentations by generators and relations for the rook partition monoids and algebras, as well as their singular ideals.  ...  Among other results, we also calculate the minimal sizes of generating sets (some of our presentations use such minimal-size generating sets), and show that the singular part of the rook partition monoid  ...  With respect to the partition algebras in particular, we refer to the recent work of Enyang on Jucys-Murphy elements [25] and seminormal forms [26] , in which the presentations from [20, 37] played  ... 
arXiv:1606.00563v1 fatcat:gvjsxxwyhzgepagyvblg335kqm

Representations of the q-rook monoid

Tom Halverson
2004 Journal of Algebra  
The q-rook monoid I n (q) is a semisimple algebra over C(q) that specializes when q → 1 to C[R n ], where R n is the monoid of n × n matrices with entries from {0, 1} and at most one nonzero entry in each  ...  When q is specialized to a prime power, is the monoid of n × n matrices with entries from a finite field having q-elements and B ⊆ M is the Borel subgroup of invertible upper triangular matrices.  ...  I also thank Momar Dieng, whose work on the characters of I n (q) in [4] helped lead to the presentation (2.1) and to the calculations in Remark 4.4.  ... 
doi:10.1016/j.jalgebra.2003.11.002 fatcat:4yo24dodrzg2lojklyxwahrupi