Rational function certification of multisum/integral/``$q$'' identities

Principal subspaces of basic modules for twisted affine Lie algebras, $q$-series multisums, and Nandi's identities

We provide an observation relating several known and conjectured $q$-series identities to the theory of principal subspaces of basic modules for twisted affine Lie algebras. We also state and prove two new families of $q$-series identities. The first family provides quadruple sum representations for Nandi's identities, including a manifestly positive representation for the first identity. The second is a family of new mod 10 identities connected with principal characters of level 4 integrable, highest-weight modules of $\mathrm{D}_4^{(3)}$.

惰性二次序的多个罗杰斯-拉马努金型恒等式

Multiple Rogers-Ramanujan type identities for inert quadratic orders

本文计算了惰性二次序的Quot和有限化Coh zeta函数并将其表示为2m重多重和，证明该多重和等于m重Bressoud和以验证猜想，还通过引入幽灵参数推广多重和并证明其与参数无关，最后提出精炼多重和以插值三种二次序的Quot zeta函数版本。

The Bailey chain and mock theta functions

Standard applications of the Bailey chain preserve mixed mock modularity but not mock modularity. After illustrating this with some examples, we show how to use a change of base in Bailey pairs due to Bressoud, Ismail and Stanton to explicitly construct families of q-hypergeometric multisums which are mock theta functions. We also prove identities involving some of these multisums and certain classical mock theta functions.

Quiver mutation sequences and $q$-binomial identities

In this paper, first we introduce a quantity called a partition function for a quiver mutation sequence. The partition function is a generating function whose weight is a $q$-binomial associated with each mutation. Then, we show that the partition function can be expressed as a ratio of products of quantum dilogarithms. This provides a systematic way of constructing various $q$-binomial multisum identities.

Partial theta functions. I. Beyond the lost notebook

It is shown how many of the partial theta function identities in Ramanujan's lost notebook can be generalized to infinite families of such identities. Key in our construction is the Bailey lemma and a new generalization of the Jacobi triple product identity. By computing residues around the poles of our identities we find a surprising connection between partial theta functions identities and Garret-Ismail-Stanton-type extensions of multisum Rogers-Ramanujan identities.

关于$2$级$A_{2\ell-1}^{(2)}$主特征的四个Takigiku-Tsuchioka猜想的证明

Proofs of four Takigiku--Tsuchioka conjectures on level $2$ principal characters of $A_{2\ell-1}^{(2)}$

本研究针对Takigiku与Tsuchioka提出的四个含Rogers-Ramanujan型恒等式的猜想，运用Bailey对方法、含高斯多项式的有限和恒等式及五重积恒等式，证明了与特定级主特征相关的恒等式。