Abstract:
Two sets of identities between unitary minimal Virasoro characters at levels $m=3,4,5$ are presented and proven. The first identity suggests a connection between the Ising and tricritical Ising models since the $m=3$ Virasoro characters are obtained as bilinears of $m=4$ Virasoro characters. The second identity gives the tricritical Ising model characters as bilinears in the Ising model characters and the six combinations of $m=5$ Virasoro characters which do not appear in the spectrum of the three state Potts model. The implication of these identities on the study of the branching rules of $N=4$ superconformal characters into $\widehat{SU(2)} \times \widehat{SU(2)}$ characters is discussed.

Abstract:
We derive several identities that feature irreducible characters of the general linear, the symplectic, the orthogonal, and the special orthogonal groups. All the identities feature characters that are indexed by shapes that are "nearly" rectangular, by which we mean that the shapes are rectangles except for one row or column that might be shorter than the others. As applications we prove new results in plane partitions and tableaux enumeration, including new refinements of the Bender-Knuth and MacMahon (ex-)conjectures.

Abstract:
The theme of this paper is political identity and participation amongMuslim migrant young people in Denmark. Political identity is analysedby examining students’ political interests and perception of themselves as participants in politics, as well as their rationalities for politics. In order to address the research question ‘What characterizes political identities among Muslim immigrant young people in schools?’ we interviewed eight Muslim students from a Danish upper secondary school and from different national origins. The students’ political orientations seemed quite contradictory, even among those who might readily have been identified as a-political. Despite moderate political interest, all students showed some inclinations to participate in elections or in particular issues. However, they emphasized that their social studies classes primarily provided them with factual knowledge experience, and some students found this knowledge useful. None of the students seemed to experience school as an arena for participation. Consequently, there is first a need to emphasize the significance of a dynamic perspective on the phenomenon of political identity, and second, we need to know how students in school should be regarded as citizens in ‘the making’ or as equal citizens in a participatory arena.

Abstract:
This paper undertakes a comparative analysis of three Australian teenage novels – Melina Marchetta’s ‘Looking for Alibrandi’ (1992), Randa Abdel-Fattah’s ‘Does my Head Look Big in This?’ (2005), and Morris Gleitzman’s ‘Girl Underground’ (2004). Drawing from feminist post-structural and post-colonial theories, the paper examines how each author has constructed the racialised-gendered identities of their female protagonists, including the ways in which they struggle to develop an identity in-between minority and dominant cultures. Also considered is how each author inter-weaves race, gender and class to produce subjects that are positioned differently across minority and dominant cultures. The similarities in how the authors have inscribed race and ethnicity on the subjectivities of their female characters, despite the novels being written at different points in time and focusing on different racial and ethnic identities, suggest that what it means to be a raced subject in Australia has more to do with the significance of all-at-once ‘belonging’ and ‘not belonging’ to the dominant culture, of ‘inclusion’ and ‘exclusion’ and of ‘sameness’ and ‘otherness’, than it has with the unique characteristics of biological race and ethnic identification. The paper argues that this kind of fiction carries with it an implicit pedagogy about race relations in Australia, which has the potential to subvert oppressive binary dualisms of race and gender by demonstrating possibilities for the development of hybrid cultural identities and ‘collaborations of humanity’.

Abstract:
We state and prove various new identities involving the Z_K parafermion characters (or level-K string functions) for the cases K=4, K=8, and K=16. These identities fall into three classes: identities in the first class are generalizations of the famous Jacobi theta-function identity (which is the K=2 special case), identities in another class relate the level K>2 characters to the Dedekind eta-function, and identities in a third class relate the K>2 characters to the Jacobi theta-functions. These identities play a crucial role in the interpretation of fractional superstring spectra by indicating spacetime supersymmetry and aiding in the identification of the spacetime spin and statistics of fractional superstring states.

Abstract:
In the process of (re)constructing their identities in an alien society, South Asians have tended to give to religion a significant importance. This salience of religion owes as much to the dislocation and the stigmatization engendered by the migration experience as to the local context, the United States, who, while promoting a policy of multiculturalism, sees religion as an ‘acceptable’ identity marker. Drawing on this process, this article examines the implications on the inter-ethnic relationships, in particular between Hindus and Muslims (both Indian and Pakistani), as two opposite and competing trends are underway: on the one hand, separate, if not confrontational, Hindu and Muslim identities are arising, while on the other hand, a South Asian identity, ignoring the borders of Partition, is shaping up.

Abstract:
For p \in {3, 4} and all p' > p, with p' coprime to p, we obtain fermionic expressions for the combination \chi^{p, p'}_{1, s} + q^{\Delta} \chi^{p, p'}_{p-1,s} of Virasoro (W_2) characters for various values of s, and particular choices of Delta. Equating these expressions with known product expressions, we obtain q-series identities which are akin to the Andrews-Gordon identities. For p=3, these identities were conjectured by Bytsko. For p=4, we obtain identities whose form is a variation on that of the p=3 cases. These identities appear to be new. The case (p,p')=(3,14) is particularly interesting because it relates not only to W_2, but also to W_3 characters, and offers W_3 analogues of the original Andrews-Gordon identities. Our fermionic expressions for these characters differ from those of Andrews et al which involve Gaussian polynomials.

Abstract:
Mostly the literature of the present depicts the difference between male andfemale, the rich and the poor, colonizers and the colonized, and oppressors and theoppressed. From the rise of the feminism in the world, a variety of writers- both male andfemale, tried their level best to show the plight of women, their inferiority, economicinsecurity, social discrimination and all that. At the same time the literature of theminority was flourishing a lot stating the bad condition of the minority in their concernedstate. The women from the minority communities, particularly the black women, cameahead to assert their rights in the patriarchal society. As we say that the literature has thepower to change the society, the feminists portrayed many women characters withdifferent qualities in their works to let the world know the condition of women. Somehaving adhered to the old social structure where the role of women was bound to thehousehold work only and the others challenged the old systems and searched for the newidentity for women in the manmade world. The present paper deals with the portrayal ofvarious women characters in Monica Ali's Brick lane.

Abstract:
Verbally prime algebras are important in PI theory. They were described by Kemer over a field $K$ of characteristic zero: 0 and $K$ (the trivial ones), $M_n(K)$, $M_n(E)$, $M_{ab}(E)$. Here $K$ is the free associative algebra of infinite rank, with free generators $T$, $E$ denotes the infinite dimensional Grassmann algebra over $K$, $M_n(K)$ and $M_n(E)$ are the $n\times n$ matrices over $K$ and over $E$, respectively. The algebras $M_{ab}(E)$ are subalgebras of $M_{a+b}(E)$, see their definition below. The generic (also called relatively free) algebras of these algebras have been studied extensively. Procesi described the generic algebra of $M_n(K)$ and lots of its properties. Models for the generic algebras of $M_n(E)$ and $M_{ab}(E)$ are also known but their structure remains quite unclear. In this paper we study the generic algebra of $M_{11}(E)$ in two generators, over a field of characteristic 0. In an earlier paper we proved that its centre is a direct sum of the field and a nilpotent ideal (of the generic algebra), and we gave a detailed description of this centre. Those results were obtained assuming the base field infinite and of characteristic different from 2. In this paper we study the polynomial identities satisfied by this generic algebra. We exhibit a basis of its polynomial identities. It turns out that this algebra is PI equivalent to a 5-dimensional algebra of certain upper triangular matrices. The identities of the latter algebra have been studied; these were described by Gordienko. As an application of our results we describe the subvarieties of the variety of unitary algebras generated by the generic algebra in two generators of $M_{11}(E)$. Also we describe the polynomial identities in two variables of the algebra $M_{11}(E)$.

Abstract:
We study the Andrews-Gordon-Bressoud (AGB) generalisations of the Rogers-Ramanujan q-series identities in the context of cylindric partitions. We recall the definition of r-cylindric partitions, and provide a simple proof of Borodin's product expression for their generating functions, that can be regarded as a limiting case of an unpublished proof by Krattenthaler. We also recall the relationships between the r-cylindric partition generating functions, the principal characters of affine sl_r algebras, the M^{r, r+d}_r minimal model characters of W_r algebras, and the r-string abaci generating functions, as well as the relationships between them, providing simple proofs for each. We then set r=2, and use 2-cylindric partitions to re-derive the AGB identities as follows. Firstly, we use Borodin's product expression for the generating functions of the 2-cylindric partitions with infinitely-long parts, to obtain the product sides of the AGB identities, times a factor (q; q)_{\infty}^{-1}, which is the generating function of ordinary partitions. Next, we obtain a bijection from the 2-cylindric partitions, via 2-string abaci, into decorated versions of Bressoud's restricted lattice paths. Extending Bressoud's method of transforming between restricted paths that obey different restrictions, we obtain sum expressions with manifestly non-negative coefficients for the generating functions of the 2-cylindric partitions which contains a factor (q; q)_{\infty}^{-1}. Equating the product and sum expressions of the same 2-cylindric partitions, and canceling a factor of (q; q)_{\infty}^{-1} on each side, we obtain the AGB identities.