Preprints

M. Alvarez and P. P. Martin. A Temperley-Lieb category for 2-manifolds

preprint.

R. Marsh and P. P. Martin. Pascal arrays: counting Catalan sets

preprint.

P. P. Martin. A faithful tensor space representation for the blob algebra

preprint.

Z. Kadar, P. Martin. Geometric partition categories

preprint.

V. Koppen, J. Faria Martins, P. Martin, Exactly solvable models for 2+1D topological phases derived from crossed modules of semisimple Hopf algebras   (arxiv)

to appear .

more

Publications

F. Torzewska, J. Faria Martins, P. Martin, Motion groupoids and mapping class groupoids   (arxiv)

Communications in Math. Phys. 402 (2023) 1621-1705 .

C. Ahmed, P. Martin, V. Mazorchuk Tonal partition algebras - fundamental and geometrical aspects of representation theory   (arxiv)

Communications in Algebra 52 (2023) 233-271 .

C. Damiani, P. Martin, E.C. Rowell Generalisations of Hecke algebras from loop braid groups   (arxiv)

PJM 323 (2023) 31-65 .

C. Damiani, J. Faria Martins, P. Martin On a canonical lift of Artin's representation to loop braid groups   (arxiv)

JPAA 225 (2021) 106760 .

A. Hazi, P. Martin, A. Parker Indecomposable tilting modules for the blob algebra   (arxiv)

J Algebra 568 (2021) 273-313 .

C. Ahmed, P. Martin, V. Mazorchuk On the number of principal ideals in d-tonal partition monoids   (arxiv)

Annals of Combinatorics 25, 79 (2021) - here.

A. Bullivant, M. Calcada, Z. Kadar, P. Martin, J. Faria Martins Higher lattices, discrete two-dimensional holonomy and topological phases in (3+1) D with higher gauge symmetry

Rev Math Phys 32(4):Article number 2050011 (2020).

A. Bullivant, J. Faria Martins, P. Martin, From Aharonov-Bohm type effects in discrete (3+1)-dimensional higher gauge theory to representations of the Loop Braid Group

Advances in Theor. and Math. Phys. 23 (2019) 1685-1769.       [NOTES] (GAP snippets)

P. Martin, S.F. Zakaria Zeros of the 3-state Potts model partition function for the square lattice revisited

JSTAT (2019) 084003

A. Bullivant, A. Kimball, P. Martin, E. Rowell Representations of the necklace braid group

Commun. Math. Phys. (2019) https://doi.org/10.1007/s00220-019-03445-0

Z. Kadar, P. P. Martin and Shona Yu. On geometrically defined extensions of the Temperley-Lieb category in the Brauer category

Math. Zeitschrift http://doi.org/10.1007/s00209-019-02246-4 . (preprint update) . [NOTES].

K. Baur, P. Martin A generalised Euler-Poincaré formula for associahedra

Bull. L.M.S. DOI: 10.1112/blms.12221

O. King, P. Martin, A. Parker On central idempotents in the Brauer algebra

J. Algebra 512 (2018) 20-46.

K. Baur, P. Martin The fibres of the Scott map on polygon tilings are the flip equivalence classes

Monatshefte fur Mathematik 187 (2018) 385-424.   DOI: 10.1007/s00605-018-1209-4

A. Bullivant, M. Calcada, Z. Kadar, P. Martin, J. Faria Martins Topological phases from higher gauge symmetry in 3+1D

Phys Rev B 95 (2017), 155118.

P. P. Martin and V. Mazorchuk. Fiat categorification of the symmetric inverse semigroup ...

Semigroup Forum (2017). here

M. De Visscher and P. P. Martin. On Brauer algebra simple modules over the complex field

Trans. Amer. Math. Soc. 369 (2017), 1579-1609 . (here)

Z. Kadar, P. P. Martin, E. Rowell and Zhenghan Wang. Local representations of the loop braid group

Glasgow Math J. 59 (2017) 359-378. first view (2016). (GAP and Maxima snippets here.)

P. P. Martin and V. Mazorchuk. Partitioned Binary Relations

Mathematica Scandinavica 113 (2013) 30-52. here

P. P. Martin and V. Mazorchuk. On the representation theory of partial Brauer algebras

The Quarterly Journal of Mathematics (2013); doi: 10.1093/qmath/has043. link (abstract)

P. P. Martin. The decomposition matrices of the Brauer algebra over the complex field

Trans. Amer. Math. Soc. 367 (2015), 1797-1825 here   (preprint here is arxiv version with some of the typos fixed.)

R. M. Green, P. P. Martin and A. E. Parker. A presentation for the symplectic blob algebra

Journal of Algebra and its Applications 11 (2012) 1250060.

A. Cox, M. De Visscher and P. P. Martin. Alcove geometry and a translation principle for the Brauer algebra

Journal of Pure and Applied Algebra, 215 (2011), 335-367.

R. Marsh and P. P. Martin. Tiling bijections between paths and Brauer diagrams

Journal of Algebraic Combinatorics, 33, no. 3 (2011), 427-453.

P. P. Martin. Representation theory of a small ramified partition algebra

in NEW TRENDS IN QUANTUM INTEGRABLE SYSTEMS, Eds. M Feigin et al (World Scientific, 2010) - the Miwa Festschrift. here .

A. Cox, M. De Visscher, S. Doty and P. P. Martin. On the blocks of the walled Brauer algebra

J. Algebra 320 (2008), 169-212. (notes)

A. Cox, M. De Visscher and P. P. Martin. A geometric characterisation of the blocks of the Brauer algebra

Journal of the London Mathematical Society (2009); doi: 10.1112/jlms/jdp039 .

A. Cox, M. De Visscher and P. P. Martin. The blocks of the Brauer algebra in characteristic zero

Representation Theory 13 (2009), 272-308. [NOTES]

P. P. Martin. On diagram categories, representation theory and Statistical Mechanics

AMS Contemporary Math 456 (2008) 99-136. (on AMS/googlebooks)

Typos: p.111 line -12 "...and f o 1_s = f, 1_t o f = f whenever defined"

M. Alvarez and P. P. Martin. Higher-dimensional Temperley-Lieb algebras

J Phys A 40 (2007) F895-F909.

P. P. Martin, R. M. Green and A. E. Parker.

Towers of recollement and bases for diagram algebras: planar diagrams and a little beyond

Journal of Algebra 316 (2007) 392-452.

A. G. Cox, P. P. Martin, A. E. Parker and C. C. Xi.

Representation theory of towers of recollement: theory, notes, and examples

Journal of Algebra 302 (2006) 340-360.

R. M. Green and P. P. Martin. Constructing cell data for diagram algebras

Journal of Pure and Applied Algebra 209 (2007) 551-569.

A. Doikou and P. P. Martin.

On quantum group symmetry and Bethe ansatz for the asymmetric twin spin chain with integrable boundary

J. Stat. Mech. (2006) P06004. Journal version available here.

A. Doikou and P. P. Martin. Hecke algebra approach to the reflection equation for spin chains

J Phys A 36 (2003) 2203 .

U. Grimm and P. P. Martin. The bubble algebra: structure of a two-colour Temperley-Lieb algebra

J Phys A 36 (2003) 10551-10571 .

P. P. Martin and S. Ryom-Hansen. Virtual algebraic Lie theory: Tilting modules and Ringel duals for blob algebras

Proc. L.M.S. 89 (2004) 655-675

P. P. Martin and A. Elgamal. Ramified partition algebras

Math Z. 246 (2004) 473.

[NOTES]

A. G. Cox, J. J. Graham and P. P. Martin. The blob algebra in positive characteristic

J Alg. 266 (2003) 584-635.

P. P. Martin and D. Woodcock. Generalized blob algebras and alcove geometry

LMS JCM 6 (2003) 249-296. journal version here   ( or here )   in this volume

First arXiv version contains some typos. Details to follow.

P. P. Martin. The partition algebra and the Potts model transfer matrix spectrum in high dimensions

J. of Physics A 19 (2000), 3669-3695. (here)   (RIMS Kyoto 1995 preprint: RIMS-1022.) (NOTES)

P. P. Martin and D. Woodcock. On the structure of the blob algebra

J. of Algebra 225 (2000), 957-988.

P. P. Martin and D. Woodcock. The partition algebras and a new deformation of the Schur algebras

J. of Algebra 203 (1998), 91-124.

P. P. Martin, D. Woodcock and D. Levy. A diagrammatic approach to Hecke algebras of the reflection equation

J. of Physics A 33 (2000), 1265-1296.   ( journal version )

The formula $h^x_{ij} = h^0_{ij} +x_i -x_j$ should read $h^x_{ij} = h^0_{ij} +x_{\# i} -x_{\# j}$ where $\# i$ denotes the number of the Young diagram containing $i$ in the $d$-tuple $\lambda$.

P. P. Martin and D. Woodcock. On central idempotents in the partition algebra

J. Algebra 217 (1999), 156-169.

P. P. Martin and G. Rollet. The Potts model representation and a Robinson-Schensted correspondence for the partition algebra

Compositio Mathematica 112 (1998), 237-254.

[NOTES]

P. P. Martin and D. Woodcock. On quantum spin-chain spectra and the structure of Hecke algebras and q-groups at roots of unity

J. of Physics A 31 (1998), 10131-10154. (journal link)

P. P. Martin and B. W. Westbury. On quantum spin-chain spectra and the representation theory of Hecke algebras by augmented braid diagrams

J. of Physics A 30 (1997), 5471-5495.

P. P. Martin. The structure of the partition algebras

J. of Algebra 183 (1996), 319-358.

P. P. Martin and S. Dasmahapatra. On the algebraic approach to cubic lattice Potts models

J. of Physics A 29 (1996), 263-278.

P. P. Martin and D. Levy. Hecke algebra solutions to the reflection equation

J. of Physics A 27 (1994), L521-L526.

H. Hinrichsen, P. P. Martin, V. Rittenberg and M. Scheunert. On the two-point correlation functions for the u_q(sl_2) invariant spin one-half Heisenberg chain at roots of unity

Nucl Phys B[FS] 415 (1994), 533-556.

P. P. Martin and H. Saleur. On the exceptional structure of End_{u_q(sl_2)}(V_N^n)

Int J Mod Phys B 8 (1994), 3671-3677. ( journal version) (preprint version)

P. P. Martin and H. Saleur. On algebraic diagonalisation of the XXZ chain

Int J Mod Phys B 8 (1994), 3637-3644.

P. P. Martin and H. Saleur. Algebras in higher dimensional statistical mechanics - the exceptional partition algebras

Lett Math Phys 30 (1994), 179-185. (arXiv:hep-th/9302095v1)

P. P. Martin and H. Saleur. The blob algebra and the periodic Temperley-Lieb algebra

Lett Math Phys 30 (1994), 189-206. (arXiv:hep-th/9302094v1 )

P. P. Martin. Temperley-Lieb algebras for non-planar statistical mechanics - the partition algebra construction

JKTR 3 (1994), 51-82. (Yale CTP 1992 preprint: YCTP-P34-92.) (draft of preprint version) (journal version)

[NOTES]

P. P. Martin and H. Saleur. On an algebraic approach to higher dimensional statistical mechanics

Comm Math Phys 158 (1993), 155-190. (YCTP-P33-92.) (open access journal link)

P. P. Martin. The structure of n-variable polynomial rings as Hecke algebra modules

J Phys A 26 (1993) 7311-7324.

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others...then

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P. P. Martin and V. Rittenberg. A template for quantum spin chain spectra

Int J Mod Phys A7 Suppl.1B (1992) 707-730. ( RIMS Kyoto 1991 preprint : RIMS-770. Early draft.) NOTES.

P. P. Martin and D. S. McAnally. On commutants, dual pairs and non-semisimple algebras from Statistical Mechanics

Int J Mod Phys A7 Suppl.1B (1992) 675-705. ( RIMS Kyoto 1991 preprint : RIMS-819.)

P. P. Martin. On Schur-Weyl duality, A_n Hecke algebras and quantum sl(N) on...

Int J Mod Phys A7 Suppl.1B (1992) 645-673. ( RIMS Kyoto 1991 preprint : RIMS-782: RIMS782 colour scan.)

T. Deguchi and P. P. Martin. An algebraic approach to vertex models and transfer matrix spectra

Int J Mod Phys A7 Suppl.1A (1992) 165-196. ( RIMS Kyoto 1991 preprint : RIMS-831.) [NOTES]

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P. P. Martin. Potts models and related problems in statistical mechanics

World Scientific (1991).

[NOTES]

See here for more typos.

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OLDER PAPERS HERE

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footnotes, unpublished articles, etc
blob footnotes
brauer footnotes

P. P. Martin. Pascal's triangle and word bases for blob algebra ideals

preprint.

P. P. Martin and B.W. Westbury. On the centraliser algebras of quantum linear groups

City/Warwick preprint.

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